Phases of Lagrangian-invariant objects in the derived category of an abelian variety

Details Phases of Lagrangian-invariant objects in the derived category of an abelian variety Phases of Lagrangian-invariant objects in the derived category of an abelian variety

2012-03-11

arxiv.org/abs/1203.2300v1

Mathematics

Algebraic Geometry

48 pages

Scientific paper

We continue the study of Lagrangian-invariant objects (LI-objects for short) in the derived category $D^b(A)$ of coherent sheaves on an abelian variety, initiated in arXiv:1109.0527. For every element of the complexified ample cone $D_A$ we construct a natural phase function on the set of LI-objects, which in the case $\dim A=2$ gives the phases with respect to the corresponding Bridgeland stability (see math.AG/0307164). The construction is based on the relation between endofunctors of $D^b(A)$ and a certain natural central extension of groups, associated with $D_A$ viewed as a hermitian symmetric space.

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