# Complex Algebraic Surfaces

@inproceedings{Beauville1996ComplexAS, title={Complex Algebraic Surfaces}, author={Arnaud Beauville}, year={1996} }

Introduction Notation Part I. The Picard Group and the Riemann-Roch Theorem: Part II. Birational Maps: Part III. Ruled Surfaces: Part IV. Rational Surfaces: Part V. Castelnuovo's Theorem and Applications: Part VI. Surfaces With pg = 0 and q > 1: Part VII. Kodaira Dimension: Part VIII. Surfaces With k = 0: Part IX. Surfaces With k = 1 and Elliptic Surfaces: Part X. Surfaces of General Type: Appendix A. Characteristic p Appendix B. Complex surfaces Appendix C. Further reading References Index.

## 549 Citations

3264 and All That: A Second Course in Algebraic Geometry

- Mathematics
- 2016

Introduction 1. Introducing the Chow ring 2. First examples 3. Introduction to Grassmannians and lines in P3 4. Grassmannians in general 5. Chern classes 6. Lines on hypersurfaces 7. Singular…

On a class of algebraic surfaces with numerically effective cotangent bundles

- Mathematics
- 2006

In this dissertation, we will present two new results in complex geometry. The first one is for a borderline class of surfaces with nef cotangent bundle. The statement of the main theorem on this…

A brief survey of K3 surfaces

- Mathematics
- 2015

This monograph gives a view, from both differential and algebraic geometry, of K3 surfaces. First we build-up to the Riemann–Roch theorem on K3 surfaces, the statement of which needs several powerful…

Negative curves on algebraic surfaces

- Mathematics
- 2013

We study curves of negative self-intersection on algebraic surfaces. Our main result shows there exist smooth complex projective surfaces X, related to Hilbert modular surfaces, such that X contains…

Integrable systems and projective images of Kummer surfaces

- Mathematics
- 2000

The (-1 )-involution on the Jacobian Jr of an arbitrary Riemann surface r of genus two leads to a singular surface, the Kummer surface Icr of Jr, which, after desingularization, defines a X-3 surface…

Arrangements of curves and algebraic surfaces

- Mathematics
- 2007

We prove a strong relation between Chern and log Chern invariants of algebraic surfaces. For a given arrangement of curves, we find nonsingular projective surfaces with Chern ratio arbitrarily close…

Product-Quotient Surfaces: new invariants and algorithms

- Mathematics
- 2013

In this article we suggest a new approach to the systematic, computer-aided construction and to the classification of product-quotient surfaces, introducing a new invariant, the integer gamma, which…

Nef cones of Hilbert schemes of points on surfaces

- Mathematics
- 2015

Let X be a smooth projective surface of irregularity 0. The Hilbert scheme of n points on X parameterizes zero-dimensional subschemes of X of length n. In this paper, we discuss general methods for…

Special systems through double points on an algebraic surface

- Mathematics
- 2006

Let S be a smooth projective algebraic surface satisfying the following property: H i (S, B) = 0 for i > 0, for any irreducible and reduced curve B of S. The aim of this paper is to provide a…

ARITHMETIC OF K3 SURFACES DRAFT LECTURE NOTES

- Mathematics
- 2015

Example 1.2 (K3 surfaces of degrees 4, 6, and 8). Let X be a smooth complete intersection of type (d1, . . . , dr) in Pk , i.e., X ⊆ P has codimension r and X = H1∩· · ·∩Hr, where Hi is a…