In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves onâ€¦ (More)

Let X be a smooth projective variety over C with the (linearized) action of a complex reductive group G, and let T âŠ‚ G be a maximal torus. In this setting, there are two geometric invariant theoryâ€¦ (More)

0. Introduction. The main goal of this paper is to give a unified description for the structure of the small quantum cohomology rings for all projective homogeneous spacesSLn(C)/P , whereP is aâ€¦ (More)

In this paper we propose and discuss a mirror construction for complete intersections in partial flag manifolds F (n1, . . . , nl, n). This construction includes our previous mirror construction forâ€¦ (More)

Â§0. Introduction. The (small) quantum cohomology QHâˆ—(X) of a complex projective manifold X can be thought of either as a deformation of the even degree cohomology V := H2âˆ—(X,C) or as a family ofâ€¦ (More)

(0.1) In many moduli problems in algebraic geometry there is a difference between the actual dimension of the moduli space and the expected, or virtual dimension. When this happens, the moduliâ€¦ (More)

Following the work of Okounkov-Pandharipande [OP1, OP2] and Diaconescu [D], we study the equivariant quantum cohomology QHâˆ— (Câˆ—)2(Hilbn) of the Hilbert scheme and the relative Donaldson-Thomas theoryâ€¦ (More)

Part (B) leads to well known difficulties which in algebraic geometry are resolved by using the language of stacks. This can be seen as passing to the nonabelian left derived functor of (B). Indeed,â€¦ (More)

We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res.â€¦ (More)