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Classical aspects of quantum cohomology of generalized flag varieties
Gromov-Witten invariants Quantum cohomology Flag varieties
2011/9/20
Abstract: We show that various genus zero Gromov-Witten invariants for flag varieties representing different homology classes are indeed the same. In particular, many of them are classical intersectio...
The generalized Hodge and Bloch conjectures are equivalent for general complete intersections
The generalized Hodge Bloch conjectures general complete intersections Algebraic Geometry
2011/9/5
Abstract: Let $X$ be a smooth complex projective variety with trivial Chow groups. (By trivial, we mean that the cycle class is injective.) We show (assuming the Lefschetz standard conjecture) that if...
On the generalized integrable Chaplygin system
integrable Chaplygin system algebraic curves
2010/4/1
We discuss two polynomial bi-Hamiltonian structures for the generalized integrable Chaplygin system on the sphere S^2 with an additional integral of fourth order in momenta. An explicit procedure to f...