scholarly journals Hitchin Fibrations on Two-Dimensional Moduli Spaces of Irregular Higgs Bundles with One Singular Fiber

2019 ◽  
Author(s):  
Péter Ivanics ◽  
◽  
András I. Stipsicz ◽  
Szilárd Szabó ◽  
◽  
...  
Keyword(s):  
Moduli Spaces ◽  
Two Dimensional ◽  
Higgs Bundles ◽  
Singular Fiber

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 Areas of two-dimensional moduli spaces

2001 ◽  
Vol 129 (11) ◽  
pp. 3241-3252 ◽  
Author(s):  
Toshihiro Nakanishi ◽  
Marjatta Näätänen
Keyword(s):  
Moduli Spaces ◽  
Two Dimensional

Involutions of Higgs moduli spaces over elliptic curves and pseudo-real Higgs bundles

2019 ◽  
Vol 142 ◽  
pp. 47-65 ◽  
Author(s):  
Indranil Biswas ◽  
Luis Angel Calvo ◽  
Emilio Franco ◽  
Oscar García-Prada
Keyword(s):  
Elliptic Curves ◽  
Moduli Spaces ◽  
Higgs Bundles

Moduli of wild Higgs bundles on with -actions

2021 ◽  
pp. 1-34
Author(s):  
LAURA FREDRICKSON ◽  
ANDREW NEITZKE
Keyword(s):  
Fixed Points ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Central Charge ◽  
Higgs Field ◽  
Vertex Algebra ◽  
Higgs Bundles ◽  
Irregular Singularity ◽  
Isomorphism Classes ◽  
Type Decomposition

Abstract We study a set $\mathcal{M}_{K,N}$ parameterising filtered SL(K)-Higgs bundles over $\mathbb{C}P^1$ with an irregular singularity at $z = \infty$ , such that the eigenvalues of the Higgs field grow like $\vert \lambda \vert \sim \vert z^{N/K} \mathrm{d}z \vert$ , where K and N are coprime. $\mathcal{M}_{K,N}$ carries a $\mathbb{C}^\times$ -action analogous to the famous $\mathbb{C}^\times$ -action introduced by Hitchin on the moduli spaces of Higgs bundles over compact curves. The construction of this $\mathbb{C}^\times$ -action on $\mathcal{M}_{K,N}$ involves the rotation automorphism of the base $\mathbb{C}P^1$ . We classify the fixed points of this $\mathbb{C}^\times$ -action, and exhibit a curious 1-1 correspondence between these fixed points and certain representations of the vertex algebra $\mathcal{W}_K$ ; in particular we have the relation $\mu = {k-1-c_{\mathrm{eff}}}/{12}$ , where $\mu$ is a regulated version of the L 2 norm of the Higgs field, and $c_{\mathrm{eff}}$ is the effective Virasoro central charge of the corresponding W-algebra representation. We also discuss a Białynicki–Birula-type decomposition of $\mathcal{M}_{K,N}$ , where the strata are labeled by isomorphism classes of the underlying filtered vector bundles.

scholarly journals Moduli space holography and the finiteness of flux vacua

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Thomas W. Grimm
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Boundary Data ◽  
Hodge Theory ◽  
Two Dimensional ◽  
Hodge Conjecture ◽  
String Compactifications ◽  
Finiteness Result ◽  
Dimensional Gravity ◽  
Dimension One

Abstract A holographic perspective to study and characterize field spaces that arise in string compactifications is suggested. A concrete correspondence is developed by studying two-dimensional moduli spaces in supersymmetric string compactifications. It is proposed that there exist theories on the boundaries of each moduli space, whose crucial data are given by a Hilbert space, an Sl(2, ℂ)-algebra, and two special operators. This boundary data is motivated by asymptotic Hodge theory and the fact that the physical metric on the moduli space of Calabi-Yau manifolds asymptotes near any infinite distance boundary to a Poincaré metric with Sl(2, ℝ) isometry. The crucial part of the bulk theory on the moduli space is a sigma model for group-valued matter fields. It is discussed how this might be coupled to a two-dimensional gravity theory. The classical bulk-boundary matching is then given by the proof of the famous Sl(2) orbit theorem of Hodge theory, which is reformulated in a more physical language. Applying this correspondence to the flux landscape in Calabi-Yau fourfold compactifications it is shown that there are no infinite tails of self-dual flux vacua near any co-dimension one boundary. This finiteness result is a consequence of the constraints on the near boundary expansion of the bulk solutions that match to the boundary data. It is also pointed out that there is a striking connection of the finiteness result for supersymmetric flux vacua and the Hodge conjecture.

scholarly journals Moduli Spaces of Higgs Bundles – Old and New

2021 ◽  
Author(s):  
Jan Swoboda
Keyword(s):  
Moduli Spaces ◽  
Higgs Bundles ◽  
Open Problems

AbstractWe give an overview of the differential geometric and analytic aspects of Higgs bundles and their moduli spaces and highlight some of their interrelations with neighboring fields. We review various current developments in this subject and provide a discussion of a number of open problems.

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