A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck’s Quot scheme. Over nodal curves, a relative… (More)

We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a trivial bundle on a smooth projective curve. We use the virtual localization formula to calculate virtual… (More)

The purpose of this paper is twofold. First, we survey known results about theta dualities on moduli spaces of sheaves on curves and surfaces. Secondly, we establish new such dualities in the surface… (More)

We present a localization proof of the fact that the cohomology of the moduli spaces of genus zero stable maps to projective spaces is entirely tautological. In addition, we obtain a description of a… (More)

We study the tautological rings of the moduli spaces of genus zero stable maps. We show that the rational cohomology of the genus zero stable map spaces to SL flag varieties is entirely tautological.… (More)

We determine generators for the codimension 1 Chow group of the moduli spaces of genus zero stable maps to flag varieties G/P . In the case of SL flags, we find all relations between our generators,… (More)

We show that intersection numbers on the moduli space of stable bundles of coprime rank and degree over a smooth complex curve can be recovered as highestdegree asymptotics in formulas of… (More)

We extend results on generic strange duality for K3 surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized K3s. We… (More)

We present a localization proof of the fact that the cohomology of the moduli spaces of genus zero stable maps to projective spaces is entirely tautological. In addition, we obtain a description of a… (More)

We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of… (More)