Certain moduli spaces for bundles on elliptic surfaces with p g = 1

1993 ◽  
pp. 57-98
Author(s):  
John W. Morgan ◽  
Kieran G. O’Grady
Keyword(s):  
Moduli Spaces ◽  
Elliptic Surfaces

scholarly journals $$\pi _1$$ of Miranda moduli spaces of elliptic surfaces

2021 ◽  
Author(s):  
Michael Lönne
Keyword(s):  
Fundamental Group ◽  
Moduli Spaces ◽  
Classical Result ◽  
Projective Line ◽  
The Other ◽  
Fundamental Groups ◽  
Elliptic Surfaces ◽  
Generators And Relations ◽  
Moduli Stacks ◽  
Finite Presentations

AbstractWe give finite presentations for the fundamental group of moduli spaces due to Miranda of smooth Weierstrass curves over $${\mathbf {P}}^1$$ P 1 which extend the classical result for elliptic curves to the relative situation over the projective line. We thus get natural generalisations of $$SL_2{{\mathbb {Z}}}$$ S L 2 Z presented in terms of $$\Bigg (\begin{array}{ll} 1&{}1\\ 0&{}1\end{array} \Bigg )$$ ( 1 1 0 1 ) , $$\Bigg (\begin{array}{ll} 1&{}0\\ {-1}&{}1\end{array} \Bigg )$$ ( 1 0 - 1 1 ) on one hand and the first examples of fundamental groups of moduli stacks of elliptic surfaces on the other.Our approach exploits the natural $${\mathbb {Z}}_2$$ Z 2 -action on Weierstrass curves and the identification of $${\mathbb {Z}}_2$$ Z 2 -fixed loci with smooth hypersurfaces in an appropriate linear system on a projective line bundle over $${{\mathbf {P}}}^1$$ P 1 . The fundamental group of the corresponding discriminant complement can be presented in terms of finitely many generators and relations using methods in the Zariski tradition.

scholarly journals Some notes on the moduli of stable sheaves on elliptic surfaces

1999 ◽  
Vol 154 ◽  
pp. 73-102 ◽  
Author(s):  
Kōta Yoshioka
Keyword(s):  
Moduli Spaces ◽  
Abelian Surfaces ◽  
Elliptic Surfaces ◽  
Picard Groups ◽  
Higher Rank ◽  
Stable Sheaves

AbstractIn this paper, we shall consider the birational structure of moduli of stable sheaves on elliptic surfaces, which is a generalization of Friedman’s results to higher rank cases. As applications, we show that some moduli spaces of stable sheaves on ℙ2 are rational. We also compute the Picard groups of those on Abelian surfaces.

Stable Parabolic Bundles over Elliptic Surfaces and over Riemann Surfaces

2000 ◽  
Vol 43 (2) ◽  
pp. 174-182 ◽  
Author(s):  
Christian Gantz ◽  
Brian Steer
Keyword(s):  
Moduli Spaces ◽  
Riemann Surfaces ◽  
Elliptic Surfaces ◽  
Parabolic Bundles

AbstractWe show that the use of orbifold bundles enables some questions to be reduced to the case of flat bundles. The identification of moduli spaces of certain parabolic bundles over elliptic surfaces is achieved using this method.

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.

scholarly journals EXTREMAL CASES OF RAPOPORT–ZINK SPACES

2021 ◽  
pp. 1-56
Author(s):  
Ulrich Görtz ◽  
Xuhua He ◽  
Michael Rapoport
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Complete List ◽  
Qualitative Properties ◽  
Model Case ◽  
Divisible Groups

Abstract We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the dimension of this underlying scheme is zero (resp., those where the dimension is the maximal possible). The model case for the first alternative is the Lubin–Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.

scholarly journals Obstruction theory for moduli spaces of framed flags of sheaves on the projective plane

2021 ◽  
pp. 104255
Author(s):  
Rodrigo A. von Flach ◽  
Marcos Jardim ◽  
Valeriano Lanza
Keyword(s):  
Projective Plane ◽  
Moduli Spaces ◽  
Obstruction Theory
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