Showing papers by "Valery A. Lunts published in 1998"
Journal Article•
TL;DR: The notion of mirror symmetry for abelian varieties has been studied in this article, where the authors show that the group of autoequivalences of the bounded derived category of coherent sheaves acts on the total cohomology of an abelians variety via algebraic correspondences.
Abstract: We work out the notion of mirror symmetry for abelian varieties and study its properties. Our construction are based on the correspondence between two $Q$--algebraic groups. One is the Hodge (or special Mumford--Tate) group. The second group $\bar{Spin(A)}$ is defined as follows: the group of autoequivalences of the bounded derived category of coherent sheaves acts on the total cohomology $H(A,Q)$ of an abelian variety $A$ via algebraic correspondences. The group $\bar{Spin(A)}$ is now the Zariski closure of its image in $GL(H(A,Q))$. Our constructions are compatible with the picture of mirror symmetry sketched by Kontsevich, Morrison, and others.
57 citations
Posted Content•
TL;DR: The notion of mirror symmetry for abelian varieties has been studied in this article, where the authors show that the group of autoequivalences of the bounded derived category of coherent sheaves acts on the total cohomology of an abelians variety via algebraic correspondences.
Abstract: We work out the notion of mirror symmetry for abelian varieties and study its properties. Our construction are based on the correspondence between two $Q$--algebraic groups. One is the Hodge (or special Mumford--Tate) group. The second group $\bar{Spin(A)}$ is defined as follows: the group of autoequivalences of the bounded derived category of coherent sheaves acts on the total cohomology $H(A,Q)$ of an abelian variety $A$ via algebraic correspondences. The group $\bar{Spin(A)}$ is now the Zariski closure of its image in $GL(H(A,Q))$. Our constructions are compatible with the picture of mirror symmetry sketched by Kontsevich, Morrison, and others.
10 citations