Results 31 to 40 of about 76 (73)

Quasimaps to moduli spaces of sheaves

Forum of Mathematics, Pi
We develop a theory of quasimaps to a moduli space of sheaves M on a surface S. Under some assumptions, we prove that moduli spaces of quasimaps are proper and carry a perfect obstruction theory.
Denis Nesterov
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We give a new proof of an unpublished result of Dale Peterson, proved by Lam and Shimozono, which identifies explicitly the structure constants, with respect to the quantum Schubert basis, for the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 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

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
doaj   +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

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