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Let $\nabla$ be a meromorphic connection on a vector bundle over a compact Riemann surface $\Gamma$. An automorphism $\sigma:\Gamma\to\Gamma$ is called a symmetry of $\nabla$ if the pull-back bundle and the pull-back connection can be…

Algebraic Geometry · Mathematics 2010-09-07 Camilo Sanabria

We construct geometric categorical Lie algebra actions on the derived category of coherent sheaves on Nakajima quiver varieties. These actions categorify Nakajima's construction of Kac-Moody algebra representations on the K-theory of quiver…

Algebraic Geometry · Mathematics 2011-04-05 Sabin Cautis , Joel Kamnitzer , Anthony Licata

Let $\Omega \subset \mathbb{C}^m$ be an open, connected and bounded set and $\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on $\Omega$. In this article we study quotient Hilbert modules obtained from submodules,…

Functional Analysis · Mathematics 2021-04-06 Prahllad Deb

We find certain relations between flag Hilbert schemes of points on plane curves and moduli spaces of one-dimensional plane sheaves. We show that some of these moduli spaces are unirational.

Algebraic Geometry · Mathematics 2017-01-31 Mario Maican

We prove a theorem on how a conclusion on homological dimension of a family of coherent sheaves over a scheme can be done from homological dimension of the restriction of this family to the reduction of the base.

Algebraic Geometry · Mathematics 2014-12-09 Nadezda V. Timofeeva

We define a one-dimensional family of "Euler" stability conditions on $\mathbb{P}^n$ which are conjectured to converge to Gieseker stability for coherent sheaves. Here, we focus on ${\mathbb P}^3$, first identifying Euler stability…

Algebraic Geometry · Mathematics 2022-01-03 Dapeng Mu

We study moduli space of higher rank marginally stable pairs (E,s:= (s_1,..., s_r)) consisting of torsion free coherent sheaf E of rank r and r sections (s_1,..., s_r) on a smooth projective surface. Having fixed the Chern character of E,…

Algebraic Geometry · Mathematics 2026-01-05 Caucher Birkar , Jia Jia , Artan Sheshmani , Chengxi Wang

The equivariant and ordinary cohomology rings of Hilbert schemes of points on the minimal resolution C^2//G for cyclic G are studied using vertex operator technique, and connections between these rings and the class algebras of wreath…

Quantum Algebra · Mathematics 2011-11-10 Zhenbo Qin , Weiqiang Wang

Let K be a CM-field, i.e., a totally complex quadratic extension of a totally real field F. Let X be a g-dimensional abelian variety admitting an algebra embedding of F into the rational endomorphisms End_Q(X) of X. Let A be the product of…

Algebraic Geometry · Mathematics 2025-09-30 Eyal Markman

In this article, we deal with the structure of the spherical Hall algebra of coherent sheaves with parabolic structures on a smooth projective curve of arbitrary genus. We provide a shuffle-like presentation of the vector bundle part and…

Representation Theory · Mathematics 2017-10-10 Jyun-Ao Lin

Seidel-Smith and Manolescu constructed knot homology theories using symplectic fibrations whose total spaces were certain varieties of matrices. These knot homology theories were associated to $SL(n) $ and tensor products of the standard…

Quantum Algebra · Mathematics 2009-03-09 Joel Kamnitzer

For every smooth quasi-projective surface X we construct a series of P^{n-1}-functors H_{l,n}: D(X x X^[l]) --> D(X^[n+l]) between the derived categories of the Hilbert schemes of points for n>max{l,1} using the derived McKay…

Algebraic Geometry · Mathematics 2014-05-06 Andreas Krug

Let k be an algebraically closed field of characteristic p>2. By a result of Kumar and Thomsen, the standard Frobenius splitting of the affine plane induces a Frobenius splitting of the Hilbert scheme of n points in the plane. In this…

Algebraic Geometry · Mathematics 2012-10-24 Jenna Rajchgot

We introduce and study equivariant Seiberg-Witten invariants for $4$-manifolds equipped with a smooth action of a finite group $G$. Our invariants come in two types: cohomological, valued in the group cohomology of $G$ and $K$-theoretic,…

Differential Geometry · Mathematics 2024-06-04 David Baraglia

The modified Macdonald functions $\widetilde{H}_{\mu}$ are fundamental objects in modern algebraic combinatorics. Haiman showed that there is a correspondence between the $(\mathbb{C}^{*})^2$-fixed points $I_{\mu}$ of the Hilbert schemes…

Combinatorics · Mathematics 2024-10-18 Daniel Orr , Milo Bechtloff Weising

We compute (algebraically) the Euler characteristic of a complex of sheaves with constructible cohomology. A stratified Poincar\'e-Hopf formula is then a consequence of the smooth Poincar\'e-Hopf theorem and of additivity of the…

Algebraic Topology · Mathematics 2009-05-29 Stéphane Simon

We introduce a family of varieties $Y_{n,\lambda,s}$, which we call the \emph{$\Delta$-Springer varieties}, that generalize the type A Springer fibers. We give an explicit presentation of the cohomology ring $H^*(Y_{n,\lambda,s})$ and show…

Algebraic Geometry · Mathematics 2023-08-29 Sean T. Griffin , Jake Levinson , Alexander Woo

To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…

Algebraic Geometry · Mathematics 2025-11-17 Pieter Belmans , Shinnosuke Okawa , Andrea T. Ricolfi

We define hypersymplectic structures on Lie algebroids recovering, as particular cases, all the classical results and examples of hypersymplectic structures on manifolds. We prove a 1-1 correspondence theorem between hypersymplectic…

Symplectic Geometry · Mathematics 2015-06-15 P. Antunes , J. M. Nunes da Costa

Let f: V --> U be a smooth non-isotrivial family of canonically polarized n-dimensional complex manifolds, where U is the complement of a normal crossing divisor S in a projective manifold Y. We show that some symmetric product of the sheaf…

Algebraic Geometry · Mathematics 2007-05-23 Eckart Viehweg , Kang Zuo
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