A scrapbook of complex curve theory
著者
書誌事項
A scrapbook of complex curve theory
(The University series in mathematics)
Plenum Press, c1980
大学図書館所蔵 全56件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Bibliography: p. 181
Includes index
内容説明・目次
内容説明
This is a book of "impressions" of a journey through the theory of com- plex algebraic curves. It is neither self-contained, balanced, nor particularly tightly organized. As with any notebook made on a journey, what appears is that which strikes the writer's fancy. Some topics appear because of their compelling intrinsic beauty. Others are left out because, for all their impor- tance, the traveler found them boring or was too dull or lazy to give them their due. Looking back at the end of the journey, one can see that a common theme in fact does emerge, as is so often the case; that theme is the theory of theta functions. In fact very much of the material in the book is prepara- tion for our study of the final topic, the so-called Schottky problem. More than once, in fact, we tear ourselves away from interesting topics leading elsewhere and return to our main route.
目次
* One Conics.- 1.1. Hyperbola Shadows.- 1.2. Real Projective Space, The "Unifier".- 1.3. Complex Projective Space, The Great "Unifier".- 1.4. Linear Families of Conics.- 1.5. The Mystic Hexagon.- 1.6. The Cross Ratio.- 1.7. Cayley's Way of Doing Geometries of Constant Curvature.- 1.8. Through the Looking Glass.- 1.9. The Polar Curve.- 1.10. Perpendiculars in Hyperbolic Space.- 1.11. Circles in the K-Geometry.- 1.12. Rational Points on Conics.- Two * Cubics.- 2.1. Inflection Points.- 2.2. Normal Form for a Cubic.- 2.3. Cubics as Topological Groups.- 2.4. The Group of Rational Points on a Cubic.- 2.5. A Thought about Complex Conjugation.- 2.6. Some Meromorphic Functions on Cubics.- 2.7. Cross Ratio Revisited, A Moduli Space for Cubics.- 2.8. The Abelian Differential on a Cubic.- 2.9. The Elliptic Integral.- 2.10. The Picard-Fuchs Equation.- 2.11. Rational Points on Cubics over Fp.- 2.12. Manin's Result: The Unity of Mathematics.- 2.13. Some Remarks on Serre Duality.- Three * Theta Functions.- 3.1. Back to the Group Law on Cubics.- 3.2. You Can't Parametrize a Smooth Cubic Algebraically.- 3.3. Meromorphic Functions on Elliptic Curves.- 3.4. Meromorphic Functions on Plane Cubics.- 3.5. The Weierstrass p-Function.- 3.6. Theta-Null Values Give Moduli of Elliptic Curves.- 3.7. The Moduli Space of "Level-Two Structures" on Elliptic Curves.- 3.8. Automorphisms of Elliptic Curves.- 3.9. The Moduli Space of Elliptic Curves.- 3.10. And So, By the Way, We Get Picard's Theorem.- 3.11. The Complex Structure of M.- 3.12. The j-Invariant of an Elliptic Curve.- 3.13. Theta-Nulls as Modular Forms.- 3.14. A Fundamental Domain for ?2.- 3.15. Jacobi's Identity.- Four * The Jacobian Variety.- 4.1. Cohomology of a Complex Curve.- 4.2. Duality.- 4.3. The Chern Class of a Holomorphic Line Bundle.- 4.4. Abel's Theorem for Curves.- 4.5. The Classical Version of Abel's Theorem.- 4.6. The Jacobi Inversion Theorem.- 4.7. Back to Theta Functions.- 4.8. The Basic Computation.- 4.9. Riemann's Theorem.- 4.10. Linear Systems of Degree g.- 4.11. Riemann's Constant.- 4.12. Riemann's Singularities Theorem.- Five * Quartics and Quintics.- 5.1. Topology of Plane Quartics.- 5.2. The Twenty-Eight Bitangents.- 5.3. Where Are the Hyperelliptic Curves of Genus 3?.- 5.4. Quintics.- Six * The Schottky Relation.- 6.1. Prym Varieties.- 6.2. Riemann's Theta Relation.- 6.3. Products of Pairs of Theta Functions.- 6.4. A Proportionality Theorem Relating Jacobians and Pryms.- 6.5. The Proportionality Theorem of Schottky-Jung.- 6.6. The Schottky Relation.- References.
「Nielsen BookData」 より