Picture 1 of 1
Algebraic Curves Over a Finite Field
by Hirschfeld, J. W. P.; Korchmaros,... | HC | VeryGood
Condition:
“Former library book; May have limited writing in cover pages. Pages are unmarked. ~ ”... Read moreabout condition
Shipping:
Estimated between Mon, Jun 3 and Wed, Jun 5 to 43230
Located in: Aurora, Illinois, United States
Returns:
Payments:
Shop with confidence
Seller information
- 99% positive feedback
Registered as a Business Seller
Seller assumes all responsibility for this listing.
eBay item number:375077917245
Item specifics
- Condition
- Very Good
- Seller Notes
- Binding
- Hardcover
- Weight
- 2 lbs
- Product Group
- Book
- IsTextBook
- No
- ISBN
- 9780691096797
- Publication Name
- Algebraic Curves over a Finite Field
- Item Length
- 9.5in
- Publisher
- Princeton University Press
- Publication Year
- 2008
- Series
- Princeton Series in Applied Mathematics Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 1.9in
- Item Width
- 6.5in
- Item Weight
- 41 Oz
- Number of Pages
- 744 Pages
About this product
Product Information
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of St hr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
Product Identifiers
Publisher
Princeton University Press
ISBN-10
0691096791
ISBN-13
9780691096797
eBay Product ID (ePID)
63878957
Product Key Features
Publication Name
Algebraic Curves over a Finite Field
Format
Hardcover
Language
English
Publication Year
2008
Series
Princeton Series in Applied Mathematics Ser.
Type
Textbook
Number of Pages
744 Pages
Dimensions
Item Length
9.5in
Item Height
1.9in
Item Width
6.5in
Item Weight
41 Oz
Additional Product Features
Series Volume Number
20
Lc Classification Number
Qa565
Reviews
"This book is well-written and I greatly enjoyed reading it. The wealth of information and examples in this book give the reader a firm foundation and develop an intuition for the subject. The authors have used it as a textbook for a two-year course, and it would be a fine introduction to any advanced undergraduate or graduate student wanting to learn this subject."-- Thomas Hagedorn, MAA Reviews, "This book is a self-contained guide to the theory of algebraic curves over a finite field, one that leads readers to various recent results in this and related areas. Personally I was attracted by the rich examples explained in this book." --Masaaki Homma, Kanagawa University, This book is well-written and I greatly enjoyed reading it. The wealth of information and examples in this book give the reader a firm foundation and develop an intuition for the subject. The authors have used it as a textbook for a two-year course, and it would be a fine introduction to any advanced undergraduate or graduate student wanting to learn this subject. -- Thomas Hagedorn, MAA Reviews, This book is well-written and I greatly enjoyed reading it. The wealth of information and examples in this book give the reader a firm foundation and develop an intuition for the subject. The authors have used it as a textbook for a two-year course, and it would be a fine introduction to any advanced undergraduate or graduate student wanting to learn this subject., "Very useful both for research and in the classroom. The main reason to use this book in a classroom is to prepare students for new research in the fields of finite geometries, curves in positive characteristic in a projective space, and curves over a finite field and their applications to coding theory. I think researchers will quote it for a long time." --Edoardo Ballico, University of Trento, "This book is well-written and I greatly enjoyed reading it. The wealth of information and examples in this book give the reader a firm foundation and develop an intuition for the subject. The authors have used it as a textbook for a two-year course, and it would be a fine introduction to any advanced undergraduate or graduate student wanting to learn this subject." --Thomas Hagedorn, MAA Reviews, This book is well-written and I greatly enjoyed reading it. The wealth of information and examples in this book give the reader a firm foundation and develop an intuition for the subject. The authors have used it as a textbook for a two-year course, and it would be a fine introduction to any advanced undergraduate or graduate student wanting to learn this subject. ---Thomas Hagedorn, MAA Reviews
Table of Content
Preface xi PART 1. GENERAL THEORY OF CURVES 1 Chapter 1. Fundamental ideas 3 1.1 Basic definitions 3 1.2 Polynomials 6 1.3 Affine plane curves 6 1.4 Projective plane curves 9 1.5 The Hessian curve 13 1.6 Projective varieties in higher-dimensional spaces 18 1.7 Exercises 18 1.8 Notes 19 Chapter 2. Elimination theory 21 2.1 Elimination of one unknown 21 2.2 The discriminant 30 2.3 Elimination in a system in two unknowns 31 2.4 Exercises 35 2.5 Notes 36 Chapter 3. Singular points and intersections 37 3.1 The intersection number of two curves 37 3.2 BA'ezout's Theorem 45 3.3 Rational and birational transformations 49 3.4 Quadratic transformations 51 3.5 Resolution of singularities 55 3.6 Exercises 61 3.7 Notes 62 Chapter 4. Branches and parametrisation 63 4.1 Formal power series 63 4.2 Branch representations 75 4.3 Branches of plane algebraic curves 81 4.4 Local quadratic transformations 84 4.5 Noether's Theorem 92 4.6 Analytic branches 99 4.7 Exercises 107 4.8 Notes 109 Chapter 5. The function field of a curve 110 5.1 Generic points 110 5.2 Rational transformations 112 5.3 Places 119 5.4 Zeros and poles 120 5.5 Separability and inseparability 122 5.6 Frobenius rational transformations 123 5.7 Derivations and differentials 125 5.8 The genus of a curve 130 5.9 Residues of differential forms 138 5.10 Higher derivatives in positive characteristic 144 5.11 The dual and bidual of a curve 155 5.12 Exercises 159 5.13 Notes 160 Chapter 6. Linear series and the Riemann-Roch Theorem 161 6.1 Divisors and linear series 161 6.2 Linear systems of curves 170 6.3 Special and non-special linear series 177 6.4 Reformulation of the Riemann-Roch Theorem 180 6.5 Some consequences of the Riemann-Roch Theorem 182 6.6 The Weierstrass Gap Theorem 184 6.7 The structure of the divisor class group 190 6.8 Exercises 196 6.9 Notes 198 Chapter 7. Algebraic curves in higher-dimensional spaces 199 7.1 Basic definitions and properties 199 7.2 Rational transformations 203 7.3 Hurwitz's Theorem 208 7.4 Linear series composed of an involution 211 7.5 The canonical curve 216 7.6 Osculating hyperplanes and ramification divisors 217 7.7 Non-classical curves and linear systems of lines 228 7.8 Non-classical curves and linear systems of conics 230 7.9 Dual curves of space curves 238 7.10 Complete linear series of small order 241 7.11 Examples of curves 254 7.12 The Linear General Position Principle 257 7.13 Castelnuovo's Bound 257 7.14 A generalisation of Clifford's Theorem 260 7.15 The Uniform Position Principle 261 7.16 Valuation rings 262 7.17 Curves as algebraic varieties of dimension one 268 7.18 Exercises 270 7.19 Notes 271 PART 2. CURVES OVER A FINITE FIELD 275 Chapter 8. Rational points and places over a finite field 277 8.1 Plane curves defined over a finite field 277 8.2 Fq-rational branches of a curve 278 8.3 Fq-rational places, divisors and linear series 281 8.4 Space curves over Fq 287 8.5 The StA'ohr-Voloch Theorem 292 8.6 Frobenius classicality with respect to lines 305 8.7 Frobenius classicality with respect to conics 314 8.8 The dual of a Frobenius non-classical curve 326 8.9 Exercises 327 8.10 Notes 329 Chapter 9. Zeta functions and curves with many rational points 332 9.1 The zeta function of a curve over a finite field 332 9.2 The Hasse-Weil Theorem 343 9.3 Refinements of the Hasse-Weil Theorem 348 9.4 Asymptotic bounds 353 9.5 Other estimates 356 9.6 Counting points on a plane curve 358 9.7 Further applications of the zeta function 369 9.8 The Fundamental Equation 373 9.9 Elliptic curves over Fq 378 9.10 Classification of non-singular cubics over Fq 381 9.11 Exercises 385 9.12 Notes 388 PART 3. FURTHER DEVELOPMENTS 393 Chapte
Copyright Date
2008
Topic
Algebra / Abstract, Geometry / General, Applied
Lccn
2007-940767
Dewey Decimal
516.352
Intended Audience
College Audience
Dewey Edition
22
Illustrated
Yes
Genre
Mathematics
Item description from the seller
Seller assumes all responsibility for this listing.
eBay item number:375077917245
Shipping and handling
Item location:
Aurora, Illinois, United States
Ships to:
Afghanistan, Albania, Algeria, American Samoa, Andorra, Angola, Anguilla, Antigua and Barbuda, Argentina, Armenia, Aruba, Australia, Austria, Azerbaijan Republic, Bahamas, Bahrain, Bangladesh, Belarus, Belgium, Belize, Benin, Bermuda, Bhutan, Bolivia, Bosnia and Herzegovina, Botswana, Brazil, British Virgin Islands, Brunei Darussalam, Bulgaria, Burkina Faso, Burundi, Cambodia, Cameroon, Canada, Cape Verde Islands, Cayman Islands, Central African Republic, Chad, Chile, China, Colombia, Comoros, Cook Islands, Costa Rica, Cyprus, Czech Republic, Côte d'Ivoire (Ivory Coast), Democratic Republic of the Congo, Denmark, Djibouti, Dominica, Dominican Republic, Ecuador, Egypt, El Salvador, Equatorial Guinea, Eritrea, Estonia, Ethiopia, Falkland Islands (Islas Malvinas), Fiji, Finland, France, Gabon Republic, Gambia, Georgia, Germany, Ghana, Gibraltar, Greece, Greenland, Grenada, Guam, Guatemala, Guernsey, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, Hong Kong, Hungary, Iceland, India, Indonesia, Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jersey, Jordan, Kazakhstan, Kenya, Kiribati, Kuwait, Kyrgyzstan, Laos, Latvia, Lebanon, Lesotho, Liberia, Liechtenstein, Lithuania, Luxembourg, Macau, Macedonia, Madagascar, Malawi, Malaysia, Maldives, Mali, Malta, Marshall Islands, Mauritania, Mauritius, Mayotte, Mexico, Micronesia, Moldova, Monaco, Mongolia, Montenegro, Montserrat, Morocco, Mozambique, Namibia, Nauru, Nepal, Netherlands, Netherlands Antilles, New Zealand, Nicaragua, Niger, Nigeria, Niue, Norway, Oman, Pakistan, Palau, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Poland, Portugal, Puerto Rico, Qatar, Republic of Croatia, Republic of the Congo, Romania, Rwanda, Saint Helena, Saint Kitts-Nevis, Saint Lucia, Saint Pierre and Miquelon, Saint Vincent and the Grenadines, San Marino, Saudi Arabia, Senegal, Serbia, Seychelles, Sierra Leone, Singapore, Slovakia, Slovenia, Solomon Islands, Somalia, South Africa, South Korea, Spain, Sri Lanka, Suriname, Svalbard and Jan Mayen, Swaziland, Sweden, Switzerland, Taiwan, Tajikistan, Tanzania, Thailand, Togo, Tonga, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Turks and Caicos Islands, Tuvalu, Uganda, United Arab Emirates, United Kingdom, Uruguay, Uzbekistan, Vanuatu, Vatican City State, Vietnam, Virgin Islands (U.S.), Wallis and Futuna, Western Sahara, Western Samoa, Worldwide, Yemen, Zambia, Zimbabwe
Excludes:
Barbados, French Guiana, French Polynesia, Guadeloupe, Libya, Martinique, New Caledonia, Reunion, Russian Federation, Ukraine, Venezuela
| Shipping and handling | To | Service | Delivery*See Delivery notes |
|---|---|---|---|
| Free shipping | United States | Economy Shipping | Estimated between Mon, Jun 3 and Wed, Jun 5 to 43230 |
| US $15.99 (approx C $21.92) | United States | Expedited Shipping | Estimated on or before Sat, Jun 1 to 43230 |
| Taxes |
|---|
| Seller charges sales tax in |
Sales tax for an item #375077917245
Sales tax for an item #375077917245
Seller collects sales tax for items shipped to the following provinces:
| Province | Sales Tax Rate |
|---|---|
| Missouri (MO) | 8.238% |
Return policy
| After receiving the item, contact seller within | Refund will be given as |
|---|---|
| 30 days after the buyer receives it | Money Back |
The seller is responsible for return shipping costs.
Payment details
Payment methods
Seller feedback (5,198,813)
z***z (602)- Feedback left by buyer.
Past 6 months
Verified purchase
🏆 SUPER STAR 🤩 AMAZING PHOTOS 🎯 ACCURATE DESCRIPTION ✏️ GENUINE PRODUCTS 💎 HIGH QUALITY 🍯 SUPER PRICES 💰 EASY TO WORK WITH 🍰 ECONOMY HANDLING ⏱️ FAST SHIPPING 🚀 BUBBLE PACKAGE 📦 ARRIVED WITHIN DAYS 🌎 EXCEPTIONAL COMMUNICATION 🎙️ OUTSTANDING CUSTOMER SERVICE 🛎️ GREAT SENSE OF HUMOR 🍿 TOTAL ASSET TO THE EBAY-ECO SYSTEM 🥇 SAVED SELLER 🎱 PROMT REPLY FOR RETURNS 🎯 WOULD BUY FROM AGAIN 🧲 UNDER PROMISES OVER DELIVERS ⛳️ MADE ME VERY HAPPY 🌈 LEFT POSITIVE FEEDBACK 🌼 THANK YOU! 😇 A+++
u***2 (270)- Feedback left by buyer.
Past month
Verified purchase
Outstanding seller. Fair prices that are more than reasonable in this economy. The product is in better condition than described, a true value for my money.
Packaged and shipped well shows seller has concern for the products sold to arrive in excellent condition. The seller communicated timely with progress. Highly recommend this seller & will do business again. Thank you!!⭐️⭐️⭐️⭐️⭐️
a***r (327)- Feedback left by buyer.
Past month
Verified purchase
thrift.books is an awesome place to purchase books! excellent communication! often the books arrive in better condition than described. ships very fast & the books arrive quickly! carefully packaged! +AAAAAAAAAA ebay sellers. i highly recommend thrift.books for people wanting to purchase books! reaasonable prices and shipping costs!