37 citations · 82 across the 7 of their papers we have counts for
17 papers
Orthogonal bundles on curves and theta functions
Arnaud Beauville
Let M be the moduli space of SO(r)-bundles on a curve, and L the determinant bundle on M. We define an isomorphism of H^0(M,L) onto the dual of the space of r-th order theta functi…
Vector bundles on curves and theta functions
Arnaud Beauville
This is a (short) survey lecture on the "theta map" from the moduli space of SL_r bundles on a curve C to the projective space of r-th order theta functions on JC . Some recent res…
Vector bundles and theta functions on curves of genus 2 and 3
Arnaud Beauville
Let C be a curve of genus g, and let SU(r) be the moduli space of vector bundles of rank r on C, with trivial determinant. A general E in SU(r) defines a theta divisor in the linea…
On the splitting of the Bloch-Beilinson filtration
Arnaud Beauville
For a smooth projective variety X, let CH(X) be the Chow ring (with rational coefficients) of algebraic cycles modulo rational equivalence. The conjectures of Bloch and Beilinson p…
The Coble hypersurfaces
Arnaud Beauville
Let A be an indecomposable principally polarized abelian variety of dimension g . Third order theta functions embed A in a projective space P(V_3), while second order theta functio…
Fano threefolds and K3 surfaces
Arnaud Beauville
We discuss in this note which K3 surfaces appear as anticanonical divisors in a Fano threefold. We prove in particular that a general K3 surface with given Picard lattice P and pol…