**Contemporary Mathematics**

Volume: 388;
2005;
188 pp;
Softcover

MSC: Primary 14;

Print ISBN: 978-0-8218-3719-1

Product Code: CONM/388

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-0-8218-7978-8
Product Code: CONM/388.E**

List Price: $69.00

Individual Member Price: $55.20

# Snowbird Lectures in Algebraic Geometry

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*Ravi Vakil*

A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry.

The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.

#### Table of Contents

# Table of Contents

## Snowbird Lectures in Algebraic Geometry

- Contents v6 free
- Preface vii8 free
- Rationally connected varieties 112 free
- A first glimpse at the minimal model program 1728
- Derived categories of sheaves: A skimming 4354
- 1. Lecture 1: The derived category 4354
- 2. Lecture 2: Triangles, exactness, and derived functors 4758
- 3. Lecture 3: The derived category of Pn and orthogonal decompositions 5263
- 4. Lecture 4: Serre duality and ampleness of the canonical class 5768
- 5. Lecture 5: Moduli problems and equivalences 6374
- 6. Lecture 6: Hochschild homology and cohomology 6879
- References 7485

- The arithmetic and geometry of Kobayashi hyperbolicity 7788
- Multiplier ideals in algebraic geometry 89100
- Mikhalkin's classification of M-curves in maximal position with respect to three lines 107118
- Groupoids and quotients in algebraic geometry 119130
- Two degeneration techniques for maps of curves 137148
- Rigid-analytic geometry and the uniformization of abelian varieties 145156
- Geometric invariant theory and projective toric varieties 161172
- An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson 169180

#### Readership

Graduate students and researchers interested in algebraic geometry.