Enumerative Geometry of Calabi-Yau 4-Folds

@article{Klemm2007EnumerativeGO,
  title={Enumerative Geometry of Calabi-Yau 4-Folds},
  author={Albrecht Klemm and Rahul Pandharipande},
  journal={Communications in Mathematical Physics},
  year={2007},
  volume={281},
  pages={621-653}
}
Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation.Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in $${{\mathbb{P}^5… 

Enumerative Geometry of Calabi-Yau 5-Folds

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving

Enumerative Geometry of Calabi-Yau 5-Folds R . Pandharipande and A . Zinger

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving

The Gopakumar-Vafa formula for symplectic manifolds

The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. Using the methods of

A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds

. Let G be a finite subgroup of SU p 4 q whose elements have age not larger than one. In the first part of this paper, we define K -theoretic stable pair invariants on the crepant resolution of the affine

Exact Kähler potential for Calabi-Yau fourfolds

A bstractWe study quantum Kähler moduli space of Calabi-Yau fourfolds. Our analysis is based on the recent work by Jockers et al. which gives a novel method to compute the Kähler potential on the

A conjectural formula for genus one Gromov-Witten invariants of some local Calabi-Yau n-folds

We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We

A conjectural formula for genus one Gromov-Witten invariants of some local Calabi-Yau n-folds

  • Xiaowen Hu
  • Mathematics
    Science China Mathematics
  • 2016
We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We
...

References

SHOWING 1-10 OF 59 REFERENCES

New Calculations in Gromov-Witten Theory

We use a topological framework to study descendent Gromov-Witten theory in higher genus, non-toric settings. Two geometries are considered: surfaces of general type and the Enriques Calabi-Yau

Hodge integrals and Gromov-Witten theory

Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these

Gromov–Witten invariants of a quintic threefold and a rigidity conjecture

We show that a widely believed conjecture concerning rigidity of genus-zero and -one holomorphic curves in Calabi-Yau threefolds implies a relation between the genus-one GW-invariants of a quintic

The enumerative geometry of K3 surfaces and modular forms

We prove the conjectures of Yau-Zaslow and Gottsche concerning the number curves on K3 surfaces. Specifically, let X be a K3 surface and C be a holomorphic curve in X representing a primitive

Virtual Moduli Cycles and Gromov-Witten Invariants of Noncompact Symplectic Manifolds

This paper constructs and studies the Gromov-Witten invariants and their properties for noncompact geometrically bounded symplectic manifolds. Two localization formulas for GW-invariants are also

Topological field theory and rational curves

We analyze the quantum field theory corresponding to a string propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear σ-model and

A topological view of Gromov-Witten theory

The quantum cohomology of blow-ups of P^2 and enumerative geometry

We compute the Gromov-Witten invariants of the projective plane blown up in r general points. These are determined by associativity from r+1 intial values. Applications are given to the enumeration
...