14 citations · 14 across the 1 of their papers we have counts for
6 papers
Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds
Sheldon Katz
Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds are compared. In certain situations, the Donaldson-Thomas invariants are very easy to handle…
Geometric Transitions and N=1 Quiver Theories
F. Cachazo, S. Katz, C. Vafa
We construct N=1 supersymmetric theories on worldvolumes of D5 branes wrapped around 2-cycles of threefolds which are A-D-E fibrations over a plane. We propose large N duals as geo…
Versal deformations and superpotentials for rational curves in smooth threefolds
Sheldon Katz
The versal deformation space of a smooth rational curve in a smooth complex threefold is explicitly computed under certain hypotheses. Under an additional hypothesis, the versal de…
Virtual Fundamental Classes of Zero Loci
David A. Cox, Sheldon Katz, Yuan-Pin Lee
Let V be a convex vector bundle over a smooth projective manifold X, and let Y be the subset of X which is the zero locus of a regular section of V. This mostly expository paper di…
Lie Groups, Calabi-Yau Threefolds, and F-Theory
Paul S. Aspinwall, Sheldon Katz, David R. Morrison
The F-theory vacuum constructed from an elliptic Calabi-Yau threefold with section yields an effective six-dimensional theory. The Lie algebra of the gauge sector of this theory an…
Multiple covers and the integrality conjecture for rational curves in Calabi-Yau threefolds
Jim Bryan, Sheldon Katz, Naichung Conan Leung
We study the contribution of multiple covers of an irreducible rational curve C in a Calabi-Yau threefold Y to the genus 0 Gromov-Witten invariants in the following cases. (1) If t…