scholarly journals On stable rationality of some conic bundles and moduli spaces of Prym curves

2018 ◽  
Vol 93 (1) ◽  
pp. 133-155 ◽  
Author(s):  
Christian Böhning ◽  
Hans-Christian Graf von Bothmer
Keyword(s):  
Moduli Spaces ◽  
Stable Rationality ◽  
Conic Bundles

scholarly journals STABILITY OF CONIC BUNDLES: WITH AN APPENDIX BY MUNDET I RIERA

2000 ◽  
Vol 11 (08) ◽  
pp. 1027-1055 ◽  
Author(s):  
TOMÁS L. GÓMEZ ◽  
IGNACIO SOLS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Conic Bundle ◽  
Conic Bundles ◽  
Definition Of

Roughly speaking, a conic bundle is a surface, fibered over a curve, such that the fibers are conics (not necessarily smooth). We define stability for conic bundles and construct a moduli space. We prove that (after fixing some invariants) these moduli spaces are irreducible (under some conditions). Conic bundles can be thought of as generalizations of orthogonal bundles on curves. We show that in this particular case our definition of stability agrees with the definition of stability for orthogonal bundles. Finally, in an appendix by I. Mundet i Riera, a Hitchin-Kobayashi correspondence is stated for conic bundles.

scholarly journals Stable rationality and conic bundles

2015 ◽  
Vol 365 (3-4) ◽  
pp. 1201-1217 ◽  
Author(s):  
Brendan Hassett ◽  
Andrew Kresch ◽  
Yuri Tschinkel
Keyword(s):  
Stable Rationality ◽  
Conic Bundles

scholarly journals Moduli of decorated swamps on a smooth projective curve

2015 ◽  
Vol 26 (10) ◽  
pp. 1550086 ◽  
Author(s):  
N. Beck
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Level Structure ◽  
Higgs Bundles ◽  
Smooth Projective Curve ◽  
Different Types ◽  
Git Quotient ◽  
Conic Bundles ◽  
Stability Concept

In order to unify the construction of the moduli space of vector bundles with different types of global decorations, such as Higgs bundles, framed vector bundles and conic bundles, A. H. W. Schmitt introduced the concept of a swamp. In this work, we consider vector bundles with both a global and a local decoration over a fixed point of the base. This generalizes the notion of parabolic vector bundles, vector bundles with a level structure and parabolic Higgs bundles. We introduce a notion of stability and construct the coarse moduli space for these objects as the GIT-quotient of a parameter space. In the case of parabolic vector bundles and vector bundles with a level structure our stability concept reproduces the known ones. Thus, our work unifies the construction of their moduli spaces.

scholarly journals Motivic measures of moduli spaces of 1-dimensional sheaves on rational surfaces

2018 ◽  
Vol 20 (03) ◽  
pp. 1750019 ◽  
Author(s):  
Yao Yuan
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Betti Numbers ◽  
Rational Surfaces ◽  
Stable Rationality

We study the moduli space of rank 0 semistable sheaves on some rational surfaces. We show the irreducibility and stable rationality of them under some conditions. We also compute several (virtual) Betti numbers of those moduli spaces by computing their motivic measures.

scholarly journals Stable rationality of higher dimensional conic bundles

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Hamid Ahmadinezhad ◽  
Takuzo Okada
Keyword(s):  
Vector Bundle ◽  
Canonical Divisor ◽  
Conic Bundle ◽  
Final Version ◽  
Stable Rationality ◽  
Higher Dimensional ◽  
Projective Vector ◽  
Conic Bundles

We prove that a very general nonsingular conic bundle $X\rightarrow\mathbb{P}^{n-1}$ embedded in a projective vector bundle of rank $3$ over $\mathbb{P}^{n-1}$ is not stably rational if the anti-canonical divisor of $X$ is not ample and $n\geq 3$. Comment: Final version. To appear in Epijournal de Geometrie Algebrique

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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