Calaque, Damien Gonzalez, Martin
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We construct a twisted version of the genus one universal Knizhnik–Zamolodchikov–Bernard (KZB) connection introduced by Calaque–Enriquez–Etingof, that we call the ellipsitomic KZB connection. This is a flat connection on a principal bundle over the moduli space of Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{...

Lasoń, Michał
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In 1980 White conjectured that every element of the toric ideal of a matroid is generated by quadratic binomials corresponding to symmetric exchanges. We prove White’s conjecture for high degrees with respect to the rank. This extends our result (Lasoń and Michałek in Adv Math 259:1–12, 2014) confirming White’s conjecture ‘up to saturation’. Furthe...

Zhang, Weiyi
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We study the moduli space of J-holomorphic subvarieties in a 4-dimensional symplectic manifold. For an arbitrary tamed almost complex structure, we show that the moduli space of a sphere class is formed by a family of linear system structures as in algebraic geometry. Among the applications, we show various uniqueness results of J-holomorphic subva...

Coates, John Li, Jianing Li, Yongxiong
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For primes q≡7mod16\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q \equiv 7 \ \mathrm {mod}\ 16$$\end{document}, the present manuscript shows that elementary methods ...

Negron, Cris
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We prove that the Drinfeld double of an arbitrary finite group scheme has finitely generated cohomology. That is to say, for G any finite group scheme, and D(G) the Drinfeld double of the group ring kG, we show that the self-extension algebra of the trivial representation for D(G) is a finitely generated algebra, and that for each D(G)-representati...

Faifman, Dmitry Wannerer, Thomas
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Any Riemannian manifold has a canonical collection of valuations (finitely additive measures) attached to it, known as the intrinsic volumes or Lipschitz–Killing valuations. They date back to the remarkable discovery of H. Weyl that the coefficients of the tube volume polynomial are intrinsic invariants of the metric. As a consequence, the intrinsi...

Benson, Dave Iyengar, Srikanth B. Krause, Henning Pevtsova, Julia
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This work concerns the representation theory and cohomology of a finite unipotent supergroup scheme G over a perfect field k of positive characteristic p≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsi...

Cheng, Jipeng Milanov, Todor
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In a companion paper (arXiv:1910.03150) to this one, we proved that the Gromov–Witten theory of a Fano orbifold line of type D is governed by a system of Hirota Bilinear Equations. The goal of this paper is to prove that every solution to the Hirota Bilinear Equations determines a solution to a new integrable hierarchy of Lax equations. We suggest ...

Johnson, Drew Oprea, Dragos Pandharipande, Rahul
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Quot schemes of quotients of a trivial bundle of arbitrary rank on a nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf has at most 1-dimensional support. The associated generating series of virtual Euler characteristics was conjectured to be a rational function in Oprea a...

Cautis, Sabin Dodd, Christopher Kamnitzer, Joel
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One of the most mysterious aspects of Saito’s theory of Hodge modules are the Hodge and weight filtrations that accompany the pushforward of a Hodge module under an open embedding. In this paper we consider the open embedding in a product of complementary Grassmannians given by pairs of transverse subspaces. The push-forward of the structure sheaf ...