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. 
3264 and All That: A Second Course in Algebraic Geometry
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
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
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
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
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
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
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
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
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
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
...
...