7 citations · 8 across the 2 of their papers we have counts for
6 papers
Gromov-Witten Invariants for Abelian and Nonabelian Quotients
Aaron Bertram, Ionut Ciocan-Fontanine, Bumsig Kim
We make precise conjectures relating the genus zero Gromov-Witten theory of a nonabelian GIT quotient X//G to that of the associated abelian quotient X//T by a maximal torus T in G…
Two Proofs of a Conjecture of Hori and Vafa
Aaron Bertram, Ionut Ciocan-Fontanine, Bumsig Kim
We give two proofs of a conjecture of Hori and Vafa which expresses the J-function (i.e, the generating function for 1-point descendant Gromov-Witten invariants) of a Grassmannian…
Using symmetry to count rational curves
Aaron Bertram
An analogy is drawn between recent work with Kley (math.AG/0007082) and the WDVV equations. That is, both are regarded as symmetries of generating functions with coefficients that…
Some applications of localization to enumerative problems
Aaron Bertram
A simple corollary of the localization theorem (due to the author and, independently, to Lian-Liu-Yau) is applied to several problems in enumerative geometry. New formulas for Schu…
New recursions for genus-zero Gromov-Witten invariants
Aaron Bertram, Holger P. Kley
New relations among the genus-zero Gromov-Witten invariants of a complex projective manifold are exhibited. When the cohomology of is generated by divisor classes and class…
On the quantum cohomology of a symmetric product of an algebraic curve
Aaron Bertram, Michael Thaddeus
The dth symmetric product of a curve of genus g is a smooth projective variety. This paper is concerned with the little quantum cohomology ring of this variety, that is, the ring h…