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Arnaud Beauville

Publications and source records attributed to Arnaud Beauville.

59 records · Page 4Linked to original sources
arXiv1996

The Picard group of the moduli of G-bundles on a curve

Let G be a complex semi-simple group, and X a compact Riemann surface. The moduli space of principal G-bundles on X, and in particular the holomorphic line bundles on this space and their global sections, play an important role in the recent applications of Conformal Field Theory to algebraic geometry. In this paper we determine the Picard group of this moduli space when G is of classical or G_2 type (we consider both the coarse moduli space and the moduli stack).

alg-geom↗
arXiv1995

Quantum cohomology of complete intersections

The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably simple form for complete intersections when the dimension is large enough w.r.t. the degree. As a reward we get a number of surprising enumerative formulas relating lines, conics and twisted cubics on X.

alg-geom↗
arXiv1994

Vector bundles on curves and generalized theta functions: recent results and open problems

Riemann surface carries a natural line bundle, the determinant bundle. The space of sections of this line bundle (or its multiples) constitutes a natural non-abelian generalization of the spaces of theta functions on the Jacobian. There has been much progress in the last few years towards a better understanding of these spaces, including a rigorous proof of the celebrated Verlinde formula which gives their dimension. This survey paper tries to explain what is now known and what remains open.

alg-geom↗
arXiv1993

Conformal blocks and generalized theta functions

Let M(r) be the moduli space of rank r vector bundles with trivial determinant on a Riemann surface X . This space carries a natural line bundle, the determinant line bundle L . We describe a canonical isomorphism of the space of global sections of L^k with a space known in conformal field theory as the ``space of conformal blocks", which is defined in terms of representations of the Lie algebra sl(r, C((z))).

alg-geom↗