On equivariant quantum cohomology
Using the Kontsevich's moduli space of stable maps, we define the equivariant quantum cohomology for generalized flag varieties and make a rigorous computation of quantum cohomology of flag varieties.
q-alg↗
arXiv subjects
Bumsig Kim
Publications and source records attributed to Bumsig Kim.
Quot schemes for flags and Gromov invariants for flag varieties
Using Quot schemes and a localization theorem we study Gromov-Witten invariants for partial flag varieties. The strategy is to extend A. Bertram's result of Gromov-Witten invariants for special Schubert varieties of Grassmannians to the case of partial flag varieties. To do so a Grothendieck's Quot scheme is generalized for flags and proven to be an irreducible, rational, smooth, projective variety following Strømme \cite{St}.
alg-geom↗
Quantum Cohomology of Partial Flag Manifolds and a Residue Formula for Their Intersection Parings
As a generalization of our previous paper [GK], we formulate a residue formula and some simple behaviors of equivariant quantum cohomology applying to compute the quantum cohomology of partial flag manifolds $F_{k_1,\cdots , k_l} $with a try to give a rigorous definition of equivariant quantum cohomology.
hep-th↗
Quantum cohomology of flag manifolds and Toda lattices
We discuss relations of Vafa's quantum cohomology with Floer's homology theory, introduce equivariant quantum cohomology, formulate some conjectures about its general properties and, on the basis of these conjectures, compute quantum cohomology algebras of the flag manifolds. The answer turns out to coincide with the algebra of regular functions on an invariant lagrangian variety of a Toda lattice.
hep-th↗