Residual categories and quantum cohomology

Abstract: Dubrovin's conjecture predicts that a smooth projective variety has a full exceptional collection in the derived category of coherent sheaves if and only if its big quantum cohomology ring is generically semisimple. However, the big quantum cohomology is very hard to compute. We suggest a conjecture, where the big quantum cohomology is replaced by the small quantum cohomology (which is much more easy to compute), and a full exceptional collection is replaced by a semiorthogonal decomposition of a special form. We support this conjecture by a number of examples provided by homogeneous varieties of simple algebraic groups. This is a joint work with Maxim Smirnov.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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