English
Related papers

Related papers: Birational Equivalences of Vortex Moduli

200 papers

Components of the Moduli space of sheaves on a K3 surface are parametrized by a lattice; the (algebraic) Mukai lattice. Isometries of the Mukai lattice often lift to symplectic birational isomorphisms of the collection of components. An…

Algebraic Geometry · Mathematics 2007-05-23 Eyal Markman

We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class…

High Energy Physics - Theory · Physics 2011-04-08 Nuno M. Romão

We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking…

Algebraic Geometry · Mathematics 2023-03-03 David Alfaya , Tomas L. Gomez

Given a Kaehlerian holomorphic fiber bundle whose fiber is a compact homogeneous Kaehler manifold, we describe the perturbed Hermitian-Einstein equations relative to certain holomorphic vector bundles. With respect to special metrics on the…

Differential Geometry · Mathematics 2007-05-23 Steven B. Bradlow , James F. Glazebrook , Franz W. Kamber

We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kaehler manifold X. These solutions are known to be related to polystable triples via a Kobayashi-Hitchin type…

Algebraic Geometry · Mathematics 2008-08-26 Indranil Biswas , Georg Schumacher

In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…

Algebraic Geometry · Mathematics 2011-11-01 D. Markushevich , A. S. Tikhomirov , G. Trautmann

We introduce Morse-type inequalities for a holomorphic circle action on a holomorphic vector bundle over a compact Kaehler manifold. Our inequalities produce bounds on the multiplicities of weights occurring in the twisted Dolbeault…

dg-ga · Mathematics 2008-02-03 Maxim Braverman

We determine all the Fourier-Mukai transforms for coherent systems consisting of a vector bundle over an elliptic curve and a subspace of its global sections, showing that these transforms are indexed by the positive integers. We prove that…

Algebraic Geometry · Mathematics 2014-02-26 Daniel Hernández Ruipérez , Carlos Tejero Prieto

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

Differential Geometry · Mathematics 2010-05-28 Janusz Grabowski , Mikolaj Rotkiewicz

In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants…

Symplectic Geometry · Mathematics 2007-05-23 Kai Cieliebak , A. Rita Gaio , Ignasi Mundet i Riera , Dietmar Salamon

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact,…

Mathematical Physics · Physics 2015-06-26 Rukmini Dey

We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be hermitian Yang-Mills, and also…

High Energy Physics - Theory · Physics 2008-11-26 Melanie Becker , Li-Sheng Tseng , Shing-Tung Yau

Assume $(X, \omega)$ is a compact symplectic manifold with a Hamiltonian compact Lie group action and the zero in the Lie algebra is a regular value of the moment map $\mu$. We prove that a finite energy symplectic vortex exponentially…

Symplectic Geometry · Mathematics 2017-07-27 Bohui Chen , Bai-Ling Wang , Rui Wang

In this paper we use the gradient flow equation introduced in [10] to construct a Morse complex for the Hamiltonian action $\mathbb A_H$ on a mixed regularity space of loops in the cotangent bundle $T^*M$ of a closed manifold $M$.…

Symplectic Geometry · Mathematics 2025-01-28 L. Asselle , M. Starostka

We give a summary of joint work with Michael Thaddeus that realizes toroidal compactifcations of split reductive groups as moduli spaces of framed bundles on chains of rational curves. We include an extension of this work that covers Artin…

Algebraic Geometry · Mathematics 2017-10-18 Johan Martens

We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…

Algebraic Topology · Mathematics 2018-05-09 Daniel A. Ramras

An action of a compact Lie group is called equivariantly formal, if the Leray--Serre spectral sequence of its Borel fibration degenerates at the E_2-term. This term is as prominent as it is restrictive. In this article, also motivated by…

Algebraic Topology · Mathematics 2019-12-17 Manuel Amann , Leopold Zoller

We previously developed an approach to Bialynicki-Birula theory for holomorphic $\mathbb{C}^*$ actions on complex analytic spaces and the concept of virtual Morse-Bott indices for singular critical points of Hamiltonian functions for the…

Differential Geometry · Mathematics 2023-07-04 Paul M. N. Feehan , Thomas G. Leness

This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of…

Algebraic Geometry · Mathematics 2018-12-11 Steven Rayan

We investigate the birational geometry (in the sense of Mori's program) of the moduli space of rank 2 semistable parabolic vector bundles on a rational curve. We compute the effective cone of the moduli space and show that all birational…

Algebraic Geometry · Mathematics 2015-07-15 Han-Bom Moon , Sang-Bum Yoo