scholarly journals THE COUPLED SEIBERG-WITTEN EQUATIONS, VORTICES, AND MODULI SPACES OF STABLE PAIRS

1995 ◽  
Vol 06 (06) ◽  
pp. 893-910 ◽  
Author(s):  
CHRISTIAN OKONEK ◽  
ANDREI TELEMAN
Keyword(s):  
Moduli Spaces ◽  
Stable Pairs

scholarly journals Moduli spaces of stable pairs

2018 ◽  
Vol 294 (1) ◽  
pp. 123-158
Author(s):  
Yinbang Lin
Keyword(s):  
Moduli Spaces ◽  
Stable Pairs

scholarly journals Some Quot schemes in tilted hearts and moduli spaces of stable pairs

2021 ◽  
Author(s):  
Franco Rota
Keyword(s):  
Moduli Spaces ◽  
Projective Variety ◽  
Smooth Projective Variety ◽  
Stability Conditions ◽  
Verlinde Formula ◽  
Quot Schemes ◽  
Text Structures ◽  
Stable Pairs ◽  
Technical Framework ◽  
Invent Math

For a smooth projective variety [Formula: see text], we study analogs of Quot schemes using hearts of non-standard [Formula: see text]-structures of [Formula: see text]. The technical framework uses families of [Formula: see text]-structures as studied in A. Bayer, M. Lahoz, E. Macrì, H. Nuer, A. Perry and P. Stellari, Stability conditions in families, preprint (2019), arXiv:1902.08184. We provide several examples and suggest possible directions of further investigation, as we reinterpret moduli spaces of stable pairs, in the sense of M. Thaddeus, Stable pairs, linear systems and the Verlinde formula, Invent. Math. 117(2) (1994) 317–353; D. Huybrechts and M. Lehn, Stable pairs on curves and surfaces, J. Algebraic Geom. 4(1) (1995) 67–104, as instances of Quot schemes.

scholarly journals Moduli of stable sheaves supported on curves of genus three contained in a quadric surface

2020 ◽  
Vol 20 (4) ◽  
pp. 507-522
Author(s):  
Mario Maican
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Betti Numbers ◽  
Free Resolutions ◽  
Quadric Surface ◽  
Arithmetic Genus ◽  
Blow Down ◽  
Stable Sheaves ◽  
Stable Pairs ◽  
Smooth Quadric Surface

AbstractWe study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of α-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description: the moduli space is obtained from a certain flag Hilbert scheme by performing two flips followed by a blow-down.

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

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