Results 51 to 60 of about 515 (73)

Transitive factorizations of permutations and geometry [PDF]

, 2014
We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves.
Goulden, I. P., Jackson, D. M.
core  

On semisimplicity of quantum cohomology of $\mathbb P^1$-orbifolds

, 2018
For a $\mathbb P^1$-orbifold $\mathscr C$, we prove that its big quantum cohomology is generically semisimple. As a corollary, we verify a conjecture of Dubrovin for orbi-curves.
Ke, Hua-Zhong
core   +1 more source

k-leaky double Hurwitz descendants

Forum of Mathematics, Sigma
We define a new class of enumerative invariants called k-leaky double Hurwitz descendants, generalizing both descendant integrals of double ramification cycles and the k-leaky double Hurwitz numbers introduced in [CMR25].
Renzo Cavalieri, Hannah Markwig, Johannes Schmitt   +2 more
doaj   +1 more source

The Betti numbers of Mbar_{0,n}(r,d)

, 2005
We calculate the Betti numbers of the coarse moduli space of stable maps of genus 0 to projective space, using a generalization of the Legendre transform.Comment: 19 ...
Getzler, E., Pandharipande, R.
core   +1 more source

A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry

, 2012
We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form $X=\mathbb{P}(K_Y\oplus\mathcal{O}_Y)$, where $Y$ is a toric Fano manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of $X$.
Auroux, Auroux, Chan, Cho, Fukaya, Kwokwai Chan, Lau   +6 more
core   +1 more source

Virasoro Constraints for Toric Bundles

Forum of Mathematics, Pi
We show that the Virasoro conjecture in Gromov–Witten theory holds for the the total space of a toric bundle $E \to B$ if and only if it holds for the base B. The main steps are: (i) We establish a localization formula that expresses Gromov–Witten
Tom Coates, Alexander Givental, Hsian-Hua Tseng   +2 more
doaj   +1 more source

Eisenstein type series for Calabi-Yau varieties

, 2010
In this article we introduce an ordinary differential equation associated to the one parameter family of Calabi-Yau varieties which is mirror dual to the universal family of smooth quintic three folds. It is satisfied by seven functions written in the $q$
Aganagic, Alim, Almkvist, Borcherds, Breuil, Candelas, Clemens, Clingher, Dijkgraaf, Doran, Douglas, Giveon, Gopakumar, Greuel, Griffiths, Hosono, Hossein Movasati, Johnsen, Kaneko, Katz, Katz, Kontsevich, Kontsevich, Krattenthaler, Morrison, Movasati, Movasati, Pandharipande, Saxl, van der Put, van Enckevort, Wiles, Yamaguchi   +32 more
core   +1 more source

A mirror theorem for Gromov-Witten theory without convexity

Forum of Mathematics, Sigma
We prove a genus zero Givental-style mirror theorem for all complete intersections in toric Deligne-Mumford stacks, which provides an explicit slice called big I-function on Givental’s Lagrangian cone for such targets.
Jun Wang
doaj   +1 more source

A geometric perspective on the piecewise polynomiality of double Hurwitz numbers [PDF]

, 2013
We describe double Hurwitz numbers as intersection numbers on the moduli space of curves. Assuming polynomiality of the Double Ramification Cycle (which is known in genera 0 and 1), our formula explains the polynomiality in chambers of double Hurwitz ...
Cavalieri, Renzo, Marcus, Steffen
core  

Logarithmic Donaldson–Thomas theory

Forum of Mathematics, Pi
Let X be a smooth and projective threefold with a simple normal crossings divisor D. We construct the Donaldson–Thomas theory of the pair $(X|D)$ enumerating ideal sheaves on X relative to D.
Davesh Maulik, Dhruv Ranganathan
doaj   +1 more source