代數(shù)幾何.I，復(fù)射影簇

內(nèi)容概要

代數(shù)幾何是近代以來發(fā)展迅速的一門數(shù)學(xué)的分支學(xué)科，與其他領(lǐng)域的許多學(xué)科有著緊密的聯(lián)系，也是高等院校數(shù)學(xué)專業(yè)研究生階段所開設(shè)的一門非常重要的基礎(chǔ)課程。 本書是時下為數(shù)不多的代數(shù)幾何的經(jīng)典教材之一，已被眾多學(xué)校用做教學(xué)參考書。與本書相配套的教材《The Red Book of Varieties and Schemes》和《Algebraic Geometry GTM52》也已影印出版。本書是由作者多年來在各處講授代數(shù)幾何課的筆記，經(jīng)多次修訂后整理成冊。全書的前一部分主要介紹了復(fù)射影簇，后一部分則重點探討了概型，內(nèi)容包括概型的凝聚層的上同調(diào)與應(yīng)用。 本書適用于數(shù)學(xué)專業(yè)的二年級研究生及需要相關(guān)知識的其他領(lǐng)域的專家學(xué)者。

作者簡介

About the Author
Biography of  David Mumford David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics. Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.

書籍目錄

IntroductionPrerequisitesChapter 1. Affine VarietiesChapter 2. Projective VarietiesChapter 3. Structure of CorrespondencesChapter 4. Chow's TheoremChapter 5. Degree of a Projective VarietyChapter 6. Linear SystemsChapter 7. Curves and Their GenusChapter 8. The Birationai Geometry of SurfacesBibliographyList of NotationsIndex

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