Sleek algebraic geometry is equipped upon primary notions: schemes and sheaves. the idea of schemes was once defined in Algebraic Geometry 1: From Algebraic types to Schemes, (see quantity 185 within the comparable sequence, Translations of Mathematical Monographs). within the current ebook, Ueno turns to the speculation of sheaves and their cohomology. Loosely talking, a sheaf is a fashion of maintaining a tally of neighborhood info outlined on a topological house, corresponding to the neighborhood holomorphic services on a fancy manifold or the neighborhood sections of a vector package. to review schemes, it truly is priceless to check the sheaves outlined on them, specially the coherent and quasicoherent sheaves. the first software in realizing sheaves is cohomology. for instance, in learning ampleness, it really is often necessary to translate a estate of sheaves right into a assertion approximately its cohomology.

The textual content covers the $64000 themes of sheaf thought, together with sorts of sheaves and the basic operations on them, corresponding to ...

coherent and quasicoherent sheaves.
proper and projective morphisms.
direct and inverse pictures.
Cech cohomology.

For the mathematician unusual with the language of schemes and sheaves, algebraic geometry can look far away. in spite of the fact that, Ueno makes the subject look common via his concise kind and his insightful factors. He explains why issues are performed this fashion and vitamins his reasons with illuminating examples. consequently, he's in a position to make algebraic geometry very available to a large viewers of non-specialists.

Show description

Read or Download Algebraic Geometry 2: Sheaves and Cohomology (Translations of Mathematical Monographs) (Vol 2) PDF

Best Algebraic Geometry books

Analytic K-Homology (Oxford Mathematical Monographs)

This paintings attracts jointly rules from algebraic topology, sensible research and geometry. it's a device - a method of conveying info between those 3 topics - and it's been used with good fortune to find theorems throughout a large span of arithmetic. the aim of this publication is to acquaint the reader with the fundamental rules of analytic K-homology and enhance a few of its functions.

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

First textbook-level account of easy examples and strategies during this sector. compatible for self-study through a reader who is familiar with a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yankee Mathematical Society, in addition to a winning Springer writer.

Hilbert

"It provides a delicate portrait of a very good person. It describes correctly and intelligibly on a nontechnical point the area of mathematical rules during which Hilbert created his masterpieces. And it illuminates the heritage of German social heritage opposed to which the drama of Hilberts existence used to be 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 limited myself to these concerns pertaining to natural research. within the moment e-book i've got defined these factor which has to be identified from geometry, seeing that research is normally constructed in this type of method that its software to geometry is proven.

Additional info for Algebraic Geometry 2: Sheaves and Cohomology (Translations of Mathematical Monographs) (Vol 2)

Show sample text content

Rated 4.81 of 5 – based on 3 votes