By Qing Liu

This new-in-paperback variation offers a normal advent to algebraic and mathematics geometry, beginning with the idea of schemes, through functions to mathematics surfaces and to the idea of aid of algebraic curves.

The first half introduces simple items reminiscent of schemes, morphisms, base switch, neighborhood homes (normality, regularity, Zariski's major Theorem). this can be via the extra international point: coherent sheaves and a finiteness theorem for his or her cohomology teams. Then follows a bankruptcy on sheaves of differentials, dualizing sheaves, and Grothendieck's duality conception. the 1st half ends with the concept of Riemann-Roch and its software to the research of gentle projective curves over a box. Singular curves are taken care of via an in depth research of the Picard group.

The moment half starts off with blowing-ups and desingularization (embedded or now not) of fibered surfaces over a Dedekind ring that leads directly to intersection conception on mathematics surfaces. Castelnuovo's criterion is proved and in addition the lifestyles of the minimum average version. This results in the examine of relief of algebraic curves. The case of elliptic curves is studied intimately. The e-book concludes with the elemental theorem of reliable relief of Deligne-Mumford.

This booklet is largely self-contained, together with the required fabric on commutative algebra. the must haves are few, and together with many examples and nearly six hundred workouts, the e-book is perfect for graduate students.

Show description

Read Online or Download Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics) PDF

Best Algebraic Geometry books

Analytic K-Homology (Oxford Mathematical Monographs)

This paintings attracts jointly principles from algebraic topology, practical research and geometry. it's a device - a way of conveying details between those 3 topics - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this ebook is to acquaint the reader with the fundamental rules of analytic K-homology and enhance a few of its purposes.

The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics)

First textbook-level account of simple examples and strategies during this region. compatible for self-study via a reader who understands a bit commutative algebra and algebraic geometry already. David Eisenbud is a widely known mathematician and present president of the yank Mathematical Society, in addition to a profitable Springer writer.


"It provides a delicate portrait of an excellent person. It describes adequately and intelligibly on a nontechnical point the area of mathematical rules during which Hilbert created his masterpieces. And it illuminates the history of German social background opposed to which the drama of Hilberts existence was once performed.

Introduction to Analysis of the Infinite: Book I

From the preface of the writer: ". .. i've got divided this paintings into books; within the first of those i've got restrained myself to these issues referring to natural research. within the moment booklet i've got defined these factor which has to be identified from geometry, due to the fact that research is as a rule built in any such approach that its program to geometry is proven.

Additional resources for Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics)

Show sample text content

Rated 4.75 of 5 – based on 30 votes