Results 41 to 50 of about 538 (92)

An introduction to the theory of Higher rank stable pairs and Virtual localization

, 2012
This article is an attempt to briefly introduce some of the results from arXiv:1011.6342 on development of a higher rank analog of the Pandharipande-Thomas theory of stable pairs on a Calabi-Yau threefold X. More precisely, we develop a moduli theory for
Sheshmani, Artan
core   +1 more source

On the asymptotic enumerativity property for Fano manifolds

Forum of Mathematics, Sigma
We study the enumerativity of Gromov–Witten invariants where the domain curve is fixed in moduli and required to pass through the maximum possible number of points.
Roya Beheshti, Brian Lehmann, Carl Lian, Eric Riedl, Jason Starr, Sho Tanimoto   +5 more
doaj   +1 more source

Higher rank sheaves on threefolds and functional equations [PDF]

Épijournal de Géométrie Algébrique, 2019
We consider the moduli space of stable torsion free sheaves of any rank on a smooth projective threefold. The singularity set of a torsion free sheaf is the locus where the sheaf is not locally free. On a threefold it has dimension $\leq 1$.
Amin Gholampour, Martijn Kool
doaj   +1 more source

Peterson-Lam-Shimozono’s theorem is an affine analogue of quantum Chevalley formula

Forum of Mathematics, Sigma
We give a new proof of an unpublished result of Dale Peterson, proved by Lam and Shimozono, which identifies explicitly the structure constants, with respect to the quantum Schubert basis, for the T-equivariant quantum cohomology $QH^{\bullet }_T(G/P)
Chi Hong Chow
doaj   +1 more source

Coordinate rings of regular nilpotent Hessenberg varieties in the open opposite schubert cell

Forum of Mathematics, Sigma
Dale Peterson has discovered a surprising result that the quantum cohomology ring of the flag variety $\operatorname {\mathrm {GL}}_n({\mathbb {C}})/B$ is isomorphic to the coordinate ring of the intersection of the Peterson variety ...
Tatsuya Horiguchi, Tomoaki Shirato
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

The KSBA moduli space of stable log Calabi–Yau surfaces

Forum of Mathematics, Pi
We prove that every irreducible component of the coarse Kollár-Shepherd-Barron and Alexeev (KSBA) moduli space of stable log Calabi–Yau surfaces admits a finite cover by a projective toric variety. This verifies a conjecture of Hacking–Keel–Yu. The proof
Valery Alexeev, Hulya Arguz, Pierrick Bousseau   +2 more
doaj   +1 more source

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  

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

Open WDVV equations and Frobenius structures for toric Calabi-Yau 3-folds

Forum of Mathematics, Sigma
Let X be a toric Calabi-Yau 3-fold and let $L\subset X$ be an Aganagic-Vafa outer brane. We prove two versions of open WDVV equations for the open Gromov-Witten theory of $(X,L)$ .
Song Yu, Zhengyu Zong
doaj   +1 more source