Books:
* Complex Algebraic Surfaces (1978) - A classic text on the theory of complex algebraic surfaces.
* Determinantal Hypersurfaces (1983) - A work focusing on the geometry of determinantal hypersurfaces.
* Algebraic Geometry (1996) - A graduate-level textbook covering fundamental concepts in algebraic geometry.
* Surfaces Algébriques (1978) - A French-language book on algebraic surfaces.
* The Geometry of K3 Surfaces (2019) - A book exploring the geometry of K3 surfaces, a specific type of complex surface.
Articles:
Beauville has also published numerous research articles in prestigious journals like Inventiones Mathematicae, Journal of the American Mathematical Society, and the Annals of Mathematics. His work has made significant contributions to:
* Moduli spaces: Spaces that parametrize geometric objects, such as curves and surfaces.
* Vector bundles: Geometric structures on manifolds that generalize the concept of tangent bundles.
* Periods of algebraic varieties: Relations between the geometry of a variety and its complex periods.
Notable Contributions:
* Beauville-Bogomolov form: A quadratic form on the cohomology of a K3 surface, used to study its geometry.
* Beauville-Laszlo theorem: A fundamental result on the moduli space of vector bundles on a curve.
* Beauville's conjecture: A conjecture about the existence of certain types of algebraic varieties.
Overall, Arnaud Beauville's work has significantly shaped the field of algebraic geometry, and his books and articles are considered essential reading for students and researchers in the area.