Related papers: Narrow quantum D-modules and quantum Serre duality

In this article, we construct an orbifold quantum cohomology twisted by a flat gerbe. Then we compute these invariants in the case of a smooth manifold and a discrete torsion on a global quotient orbifold.

Pseudocycles are geometric representatives for integral homology classes on smooth manifolds that have proved useful in particular for defining gauge-theoretic invariants. The Borel-Moore homology is often a more natural object to work with…

The wild de Rham spaces parameterize isomorphism classes of (stable) meromorphic connections, defined on principal bundles over wild Riemann surfaces. Working on the Riemann sphere, we will deformation-quantize the standard open part of de…

For a compact Lie group G we define a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundles over non-compact Kahler manifolds. The new cohomology is infinite-dimensional, but as a representation of G…

We study the quantum sheaf cohomology of flag manifolds with deformations of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds. Realized as the OPE ring…

Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. Our interest is in a sort of the linearizability problem of a neighborhood of $Y$. As a higher-codimensional generalization of Ueda's…

We study interactions between the categories of $\D$-modules on smooth and singular varieties. For a large class of singular varieties $Y$, we use an extension of the Grothendieck--Sato formula to show that $\D_Y$-modules are equivalent to…

In this paper, we focus on the moduli space of Seiberg-Witten equation on non-compact manifold with periodic end. Suppose that the scalar curvature on the periodic end is identically zero and the topological conditions: the first de-Rham…

We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement of a simple crossings symplectic divisor. We also prove…

In this paper we study various convolution-type algebras associated with a locally compact quantum group from cohomological and geometrical points of view. The quantum group duality endows the space of trace class operators over a locally…

For any smooth complex projective variety X and smooth very ample hypersurface Y in X, we develop the technique of genus zero relative Gromov-Witten invariants of Y in X in algebro-geometric terms. We prove an equality of cycles in the Chow…

The rational cohomology of the moduli space of rank two, odd degree stable bundles over a curve (of genus g > 1) has been studied intensely in recent years and in particular the invariant subring generated by Newstead's generators alpha,…

We consider a prime Fano 6-fold $Y$ of index 3, which is a fine quiver moduli space and a blow down of $\mathrm{Hilb}^3(\mathds{P}^2)$. We calculate the quantum cohomology ring of $Y$ and obtain Quantum Chevalley formulas for the Schubert…

We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional $\mathcal{N} =4$ super Yang-Mills theory on $\mathbb{CP}^{2}$ for the gauge group $SO(3)$ from the path integral of the effective…

Let E be a locally free, rank n bimodule over a smooth projective scheme X, and let A be the non-commutative symmetric algebra generated by E. We construct an internal Hom functor on the category of graded right A-modules. When E has rank…

We explain how to construct a cohomology theory on the category of separated quasi-compact smooth rigid spaces over $\mathbf{C}_p$ (or more general base fields), taking values in the category of vector bundles on the Fargues-Fontaine curve,…

We compute the quantum cohomology relative to a Lagrangian submanifold in some complete intersections. For quadric hypersurfaces, we also give a full computation of the genus zero open Gromov-Witten invariants.

We give an explicit quotient construction of the supermoduli space $\mathfrak{M}_{0, n_R}$ of genus zero super Riemann surfaces with $n_R \ge 4$ Ramond punctures and prove it is a Deligne-Mumford superstack. We also make an explicit…

In this short note, we observe that Theorem 3.1 in arXiv:1508.00682 for semiorthogonal indecomposability of the derived category of smooth DM stacks based on the canonical bundle can be extended to the case of projective varieties with…

The quantum cohomology algebra of the (full) flag manifold is a fundamental example in quantum cohomology theory, with connections to combinatorics, algebraic geometry, and integrable systems. Using a differential geometric approach, we…