Introduction to Algebraic Geometry (Dover Books on Mathematics)

Serge Lang

  • 出版商: Dover Publications
  • 出版日期: 2019-03-20
  • 售價: $710
  • 貴賓價: 9.5$675
  • 語言: 英文
  • 頁數: 272
  • 裝訂: Paperback
  • ISBN: 0486834220
  • ISBN-13: 9780486834221
  • 相關分類: 線性代數 Linear-algebra
  • 立即出貨(限量) (庫存=2)

買這商品的人也買了...

商品描述

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory.
Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

商品描述(中文翻譯)

作者Serge Lang將代數幾何定義為研究多變數代數方程組及其解的結構。這項研究可以從四個角度進行:分析、拓撲、代數幾何和算術。本書以快速、簡潔和自成一體的方式介紹了第三種方法,即代數幾何的代數方面。本書的內容假設讀者只熟悉基礎代數,包括高斯理論。

從關於位的一般理論的開篇章開始,作者進一步探討了代數變體、變體的絕對理論以及乘積、投影和對應。接下來的章節探討了正常變體、除子和線性系統、微分形式、簡單點理論以及代數群,最後聚焦於黎曼-羅赫定理。書中還包含了與代數群理論基礎相關的一般性定理。