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On the strange duality conjecture for abelian surfaces

Alina Marian, Dragos Oprea (2014)

Journal of the European Mathematical Society

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and ber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.

On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles

Fouad Elzein, András Némethi (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let Y be a normal crossing divisor in the smooth complex projective algebraic variety X and let U be a tubular neighbourhood of Y in X . Using geometrical properties of different intersections of the irreducible components of Y , and of the embedding Y X , we provide the “normal forms” of a set of geometrical cycles which generate H * ( A , B ) , where ( A , B ) is one of the following pairs ( Y , ) , ( X , Y ) , ( X , X - Y ) , ( X - Y , ) and ( U , ) . The construction is compatible with the weights in H * ( A , B , ) of Deligne’s mixed Hodge structure. The main technical part...

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