Corpus ID: 237605013

Big quantum cohomology of even dimensional intersections of two quadrics

  title={Big quantum cohomology of even dimensional intersections of two quadrics},
  author={Xiaowen Hu},
  • Xiaowen Hu
  • Published 23 September 2021
  • Mathematics
For every even dimensional smooth complete intersection, of dimension at least 4, of two quadric hypersurfaces in a projective space, we compute the genus zero Gromov-Witten invariants of length 4, and then we show that, besides a special invariant, all genus zero GromovWitten invariants can be reconstructed from the invariants of length 4. In dimension 4, we compute the special invariant by relating it to a curve counting problem. We also show that the generating function of genus zero Gromov… Expand
1 Citations
Gromov-Witten Theory of Complete Intersections
We provide an inductive algorithm computing Gromov–Witten invariants with arbitrary insertions of all smooth complete intersections in projective space, with the exception of complete intersectionsExpand


The genus 0 Gromov–Witten invariants of projective complete intersections
We describe the structure of mirror formulas for genus 0 Gromov‐Witten invariants of projective complete intersections with any number of marked points and provide an explicit algorithm for obtainingExpand
Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties
We introduce a method of constructing the virtual cycle of any scheme associated with a tangent-obstruction complex. We apply this method to constructing the virtual moduli cycle of the moduli ofExpand
Standard versus reduced genus-one Gromov–Witten invariants
We give an explicit formula for the difference between the standard and reduced genus-one Gromov‐Witten invariants. Combined with previous work on geometric properties of the latter, this paper makesExpand
Semisimple Frobenius structures at higher genus
In the context of equivariant Gromov-Witten theory of tori actions with isolated fixed points, we compute genus g > 1 Gromov-Witten potentials and their generalizations with gravitationalExpand
Quantum Cohomology of Complete Intersections
Introduction The quantum cohomology algebra of a projective manifold X is the cohomology of X endowed with a different algebra structure, which takes into account the geometry of rational curves in XExpand
Gromov-Witten classes, quantum cohomology, and enumerative geometry
The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomaticExpand
The structure of 2D semi-simple field theories
I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of κ-classes and by an extension datum to theExpand
A survey of the Hodge conjecture
Complex manifolds Vector bundles Kahler manifolds Line bundles The Lefschetz (1,1) theorem The Lefschetz (1,1) theorem revisited Formulation of the general Hodge conjecture Chern class theoryExpand
Geometry and analytic theory of Frobenius manifolds
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and ofExpand
Derived categories of quadric fibrations and intersections of quadrics
Abstract We construct a semiorthogonal decomposition of the derived category of coherent sheaves on a quadric fibration consisting of several copies of the derived category of the base of theExpand