Very stable Higgs bundles, equivariant multiplicity and mirror symmetry

Equivariant Localization and Mirror Symmetry

Mirror Symmetry and Quantum Cohomology of Projective Bundles

Abstract. In [E] we conjectured a relation between the quantum D-modules of a smooth variety X and the projectivisation of a direct sum of line bundles over it. In this paper we prove the conjecture when X is a semiample complete intersection in a toric variety. We use the conjecture to show that the relations of the small quantum cohomology ring of X that come from differential operators lift ...

The quantum equivariant cohomology of toric manifolds through mirror symmetry

Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold. e-mail address: [email protected] address: Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

Mirror Symmetry for Stable Quotients Invariants

The moduli space of stable quotients introduced by Marian-Oprea-Pandharipande provides a natural compactification of the space of morphisms from nonsingular curves to a nonsingular projective variety and carries a natural virtual class. We show that the analogue of Givental’s J-function for the resulting twisted projective invariants is described by the same mirror hypergeometric series as the ...

Mirror Symmetry for Concavex Vector Bundles on Projective Spaces

Let V + = ⊕i∈IO(ki) and V − = ⊕j∈JO(−lj) be vector bundles on P s with ki and lj positive integers. Suppose X ι →֒ Ps is the zero locus of a generic section of V + and Y is a projective manifold such that X j →֒ Y with normal bundle NX/Y = ι ∗(V −). The relations between Gromov-Witten theories of X and Y are studied here by means of a suitably defined equivariant Gromov-Witten theory in Ps. We ap...