We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on R 4 gives a deformation of the Seiberg-Wittenâ€¦ (More)

These notes have two parts. The first is a study of Nekrasov's deformed partition functions Z(Îµ 1 , Îµ 2 , a; q, Ï„) of N = 2 SUSY Yang-Mills theories , which are generating functions of theâ€¦ (More)

We continue to explore the conjectural expressions of the Gromov-Witten potentials for a class of elliptically and K3 fibered Calabi-Yau 3-folds in the limit where the base P of the K3 fibrationâ€¦ (More)

Let X be a smooth projective surface defined over C and H an ample line bundle on X . If KX is trivial, that is, X is an abelian or a K3 surface, Mukai [Mu4] introduced a quite useful notion nowâ€¦ (More)

We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on R 4 gives a deformation of the Seiberg-Wittenâ€¦ (More)

For a smooth projective toric surface we determine the Donaldson invariants and their wallcrossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture [33, 38,â€¦ (More)

In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as K-theoreticâ€¦ (More)

This is the first of two papers studying moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blowup of a projective surface. They are used toâ€¦ (More)

Chagas disease control requires an innovative approach to strengthen community participation in vector surveillance. This paper presents a case study of a community-based bug-hunting campaign inâ€¦ (More)

Let X be a smooth projective surface defined over C and H an ample line bundle on X. If KX is trivial, Mukai [M3] introduced a quite useful notion called Mukai lattice (Hev(X, Z), ã€ˆ , ã€‰), whereâ€¦ (More)