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We show that the Chow group of 0-cycles on a K3 surface contains a class of degree 1 with remarkable properties: any product of divisors is proportional to this class, and so is the second Chern
Complex Algebraic Surfaces
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
Spectral curves and the generalised theta divisor.
Let X be a smooth, irreducible, projective curve over an algebraically closed field of characteristic 0 and let g = gx ̂ 2 be its genus. We show in this paper that a generic vector b ndle on X of
Prym varieties and the Schottky problem
be the moduli space of principally polarized abelian varieties of dimension g, Jg c ~q/g the locus of Jacobians. The problem is to find explicit equations for Jg (or rather its closure Jg) in s/g. In
Conformal blocks and generalized theta functions
LetSUXr be the moduli space of rankr vector bundles with trivial determinant on a Riemann surfaceX. This space carries a natural line bundle, the determinant line bundleL. We describe a canonical
Determinantal hypersurfaces
Introduction (0.1) We discuss in this paper which homogeneous form on P n can be written as the determinant of a matrix with homogeneous entries (possibly symmetric), or the pfaaan of a
Algebraic Cycles and Motives: On the Splitting of the Bloch–Beilinson Filtration
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 predict the
Conformal blocks, fusion rules and the Verlinde formula
The Verlinde formula computes the dimension of certain vector spaces ("conformal blocks") associated to a Rational Conformal Field Theory. In this paper we show how this can be made rigorous for one
Counting rational curves on K3 surfaces
The aim of these notes is to explain the remarkable formula found by Yau and Zaslow to express the number of rational curves on a K3 surface. Projective K3 surfaces fall into countably many families
Symplectic singularities
We introduce in this paper a particular class of rational singularities, which we call symplectic, and classify the simplest ones. Our motivation comes from the analogy between rational Gorenstein