Results 41 to 50 of about 76 (73)

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We give a new proof of an unpublished result of Dale Peterson, proved by Lam and Shimozono, which identifies explicitly the structure constants, with respect to the quantum Schubert basis, for the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
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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
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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

HIGHER GENUS GROMOV–WITTEN THEORY OF $\mathsf{Hilb}^{n}(\mathbb{C}^{2})$ AND $\mathsf{CohFTs}$ ASSOCIATED TO LOCAL CURVES

Forum of Mathematics, Pi, 2019
We study the higher genus equivariant Gromov–Witten theory of the Hilbert scheme of $n$ points of $\mathbb{C}^{2}$. Since the equivariant quantum cohomology, computed by Okounkov and Pandharipande [Invent. Math.
RAHUL PANDHARIPANDE, HSIAN-HUA TSENG
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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
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GKZ Hypergeometric Structures

, 2007
This text is based on lectures by the author in the Summer School Algebraic Geometry and Hypergeometric Functions in Istanbul in June 2005. It gives a review of some of the basic aspects of the theory of hypergeometric structures of Gelfand, Kapranov ...
Stienstra, J.
core  

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

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