A support theorem for\break the Hitchin fibration: The case of GL n and K C

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mark Andrea A. de Cataldo ◽  
Jochen Heinloth ◽  
Luca Migliorini
Keyword(s):  
Moduli Spaces ◽  
Intersection Cohomology ◽  
Support Theorem ◽  
Spectral Curves ◽  
Hitchin Fibration ◽  
The One ◽  
Versal Deformations ◽  
Higgs Fields

Abstract We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GL n {\mathrm{GL}_{n}} over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every n ≥ 2 {n\geq{2}} . A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over versal deformations of spectral curves.

scholarly journals A support theorem for the Hitchin fibration: the case of

2017 ◽  
Vol 153 (6) ◽  
pp. 1316-1347
Author(s):  
Mark Andrea de Cataldo
Keyword(s):  
Analogous Result ◽  
Group Scheme ◽  
Direct Image ◽  
Support Theorem ◽  
Spectral Curves ◽  
Tate Module ◽  
Hitchin Fibration ◽  
Regularity Results ◽  
The Way

We prove that the direct image complex for the $D$-twisted $\text{SL}_{n}$ Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for $\text{GL}_{n}$ is due to Chaudouard and Laumon. Along the way, we prove that the Tate module of the relative Prym group scheme is polarizable, and we also prove $\unicode[STIX]{x1D6FF}$-regularity results for some auxiliary weak abelian fibrations.

scholarly journals Intersection cohomology of moduli spaces of sheaves on surfaces

2018 ◽  
Vol 24 (5) ◽  
pp. 3889-3926 ◽  
Author(s):  
Jan Manschot ◽  
Sergey Mozgovoy
Keyword(s):  
Moduli Spaces ◽  
Intersection Cohomology ◽  
Moduli Spaces Of Sheaves

LOW ENERGY EFFECTIVE LAGRANGIAN FOR SUPERSYMMETRIC SEESAW MODEL

2007 ◽  
Vol 16 (05) ◽  
pp. 1437-1443
Author(s):  
AKINA KATO ◽  
TAKUYA MOROZUMI ◽  
NORIMI YOKOZAKI ◽  
SYN KYU KANG
Keyword(s):  
Neutrino Mass ◽  
Higgs Mass ◽  
Higgs Sector ◽  
Low Energy ◽  
Seesaw Model ◽  
Mass Correction ◽  
Effective Lagrangian ◽  
The One ◽  
The Right ◽  
Higgs Fields

Seesaw model is an attractive model because it may explain baryogenesis through leptogenesis and also may explain the small neutrino mass. The supersymmetric seesaw model may be more attractive because the naturalness problem is absent in supersymmetric theory. Recently, the higgs mass correction due to leptons and sleptons loops is computed.1 In this talk, we report on the preliminary results on the one loop corrections of leptons and sleptons loops to the effective action of Higgs sector for super symmetric seesaw model. Our results show that the corrections to the mass parameters for Higgs sector are proportional to the soft breaking parameters of supersymmetric seesaw model, while for the quartic couplings of Higgs fields, the corrections are suppressed by inverse powers of the right-handed neutrino mass.

scholarly journals Homology TQFT's and the Alexander–Reidemeister Invariant of 3-Manifolds via Hopf Algebras and Skein Theory

2003 ◽  
Vol 55 (4) ◽  
pp. 766-821 ◽  
Author(s):  
Thomas Kerler
Keyword(s):  
Moduli Spaces ◽  
Hopf Algebras ◽  
Large Family ◽  
Quantum Invariants ◽  
Topological Quantum ◽  
Irreducible Components ◽  
Skein Theory ◽  
Higher Rank ◽  
The One ◽  
Representation Varieties

AbstractWe develop an explicit skein-theoretical algorithm to compute the Alexander polynomial of a 3-manifold from a surgery presentation employing the methods used in the construction of quantum invariants of 3-manifolds. As a prerequisite we establish and prove a rather unexpected equivalence between the topological quantum field theory constructed by Frohman and Nicas using the homology ofU(1)-representation varieties on the one side and the combinatorially constructed Hennings TQFT based on the quasitriangular Hopf algebra= ℤ/2 n ⋊ Λ* ℝ2on the other side. We find that both TQFT's are SL(2; ℝ)-equivariant functors and, as such, are isomorphic. The SL(2; ℝ)-action in the Hennings construction comes from the natural action onand in the case of the Frohman–Nicas theory from the Hard–Lefschetz decomposition of theU(1)-moduli spaces given that they are naturally Kähler. The irreducible components of this TQFT, corresponding to simple representations of SL(2; ℤ) and Sp(2g; ℤ), thus yield a large family of homological TQFT's by taking sums and products. We give several examples of TQFT's and invariants that appear to fit into this family, such as Milnor and Reidemeister Torsion, Seiberg–Witten theories, Casson type theories for homology circlesà laDonaldson, higher rank gauge theories following Frohman and Nicas, and the ℤ=pℤ reductions of Reshetikhin.Turaev theories over the cyclotomic integers ℤ[ζp]. We also conjecture that the Hennings TQFT for quantum-sl2is the product of the Reshetikhin–Turaev TQFT and such a homological TQFT.

scholarly journals Traces, high powers and one level density for families of curves over finite fields

2017 ◽  
Vol 165 (2) ◽  
pp. 225-248 ◽  
Author(s):  
ALINA BUCUR ◽  
EDGAR COSTA ◽  
CHANTAL DAVID ◽  
JOÃO GUERREIRO ◽  
DAVID LOWRY–DUDA
Keyword(s):  
Finite Field ◽  
Moduli Spaces ◽  
Function Field ◽  
Level Density ◽  
Zeta Functions ◽  
Hyperelliptic Curves ◽  
Unitary Matrix ◽  
Moduli Spaces Of Curves ◽  
A New Technique ◽  
The One

AbstractThe zeta function of a curve C over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix ΘC. We develop and present a new technique to compute the expected value of tr(ΘCn) for various moduli spaces of curves of genus g over a fixed finite field in the limit as g is large, generalising and extending the work of Rudnick [Rud10] and Chinis [Chi16]. This is achieved by using function field zeta functions, explicit formulae, and the densities of prime polynomials with prescribed ramification types at certain places as given in [BDF+16] and [Zha]. We extend [BDF+16] by describing explicit dependence on the place and give an explicit proof of the Lindelöf bound for function field Dirichlet L-functions L(1/2 + it, χ). As applications, we compute the one-level density for hyperelliptic curves, cyclic ℓ-covers, and cubic non-Galois covers.

scholarly journals Multiple Geotechnological Tools Applied to Digital Mapping of Tropical Soils

2015 ◽  
Vol 39 (5) ◽  
pp. 1261-1274 ◽  
Author(s):  
Marcelo Rodrigo Alves ◽  
José A. M. Demattê ◽  
Pedro Paulo Silva Barros
Keyword(s):  
Soil Classification ◽  
Tropical Soils ◽  
Proximal Sensing ◽  
Spectral Curves ◽  
Digital Terrain ◽  
Level 3 ◽  
Physical Attributes ◽  
The One ◽  
Terrain Elevation

ABSTRACT In recent years, geotechnologies as remote and proximal sensing and attributes derived from digital terrain elevation models indicated to be very useful for the description of soil variability. However, these information sources are rarely used together. Therefore, a methodology for assessing and specialize soil classes using the information obtained from remote/proximal sensing, GIS and technical knowledge has been applied and evaluated. Two areas of study, in the State of São Paulo, Brazil, totaling approximately 28.000 ha were used for this work. First, in an area (area 1), conventional pedological mapping was done and from the soil classes found patterns were obtained with the following information: a) spectral information (forms of features and absorption intensity of spectral curves with 350 wavelengths -2,500 nm) of soil samples collected at specific points in the area (according to each soil type); b) obtaining equations for determining chemical and physical properties of the soil from the relationship between the results obtained in the laboratory by the conventional method, the levels of chemical and physical attributes with the spectral data; c) supervised classification of Landsat TM 5 images, in order to detect changes in the size of the soil particles (soil texture); d) relationship between classes relief soils and attributes. Subsequently, the obtained patterns were applied in area 2 obtain pedological classification of soils, but in GIS (ArcGIS). Finally, we developed a conventional pedological mapping in area 2 to which was compared with a digital map, ie the one obtained only with pre certain standards. The proposed methodology had a 79 % accuracy in the first categorical level of Soil Classification System, 60 % accuracy in the second category level and became less useful in the categorical level 3 (37 % accuracy).

scholarly journals Birational Models of the Moduli Spaces of Stable Vector Bundles Over Curves

1997 ◽  
Vol 08 (06) ◽  
pp. 781-808
Author(s):  
Yi Hu ◽  
Wei-Ping Li
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Stable Vector Bundles ◽  
The One

We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in connection with rationality of moduli spaces of stable vector bundles.

scholarly journals Tropical covers of curves and their moduli spaces

2014 ◽  
Vol 17 (01) ◽  
pp. 1350045 ◽  
Author(s):  
Arne Buchholz ◽  
Hannah Markwig
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Stable Maps ◽  
Hurwitz Numbers ◽  
Polyhedral Complex ◽  
Local Duality ◽  
The One ◽  
Definition Of ◽  
Correspondence Theorem

We define the tropical moduli space of covers of a tropical line in the plane as weighted abstract polyhedral complex, and the tropical branch map recording the images of the simple ramifications. Our main result is the invariance of the degree of the branch map, which enables us to give a tropical intersection-theoretic definition of tropical triple Hurwitz numbers. We show that our intersection-theoretic definition coincides with the one given in [B. Bertrand, E. Brugallé and G. Mikhalkin, Tropical open Hurwitz numbers, Rend. Semin. Mat. Univ. Padova 125 (2011) 157–171] where a Correspondence Theorem for Hurwitz numbers is proved. Thus we provide a tropical intersection-theoretic justification for the multiplicities with which a tropical cover has to be counted. Our method of proof is to establish a local duality between our tropical moduli spaces and certain moduli spaces of relative stable maps to ℙ1.

scholarly journals EFFECTIVE ACTION OF SPONTANEOUSLY BROKEN GAUGE THEORIES

1998 ◽  
Vol 13 (01) ◽  
pp. 95-124 ◽  
Author(s):  
S.-H. HENRY TYE ◽  
YAN VTOROV-KAREVSKY
Keyword(s):  
Effective Potential ◽  
Effective Action ◽  
Gauge Theories ◽  
Perturbation Expansion ◽  
Gauge Invariant ◽  
Abelian Case ◽  
Covariant Gauge ◽  
The One ◽  
Higgs Fields ◽  
Field Redefinition

The effective action of a Higgs theory should be gauge-invariant. However, the quantum and/or thermal contributions to the effective potential seem to be gauge-dependent, posing a problem for its physical interpretation. In this paper, we identify the source of the problem and argue that in a Higgs theory perturbative contributions should be evaluated with the Higgs fields in the polar basis, not in the Cartesian basis. Formally, this observation can be made from the derivation of the Higgs theorem, which we provide. We show explicitly that, properly defined, the effective action for the Abelian Higgs theory is gauge-invariant to all orders in perturbation expansion when evaluated in the covariant gauge in the polar basis. In particular, the effective potential is gauge-invariant. We also show the equivalence between the calculations in the covariant gauge in the polar basis and the unitary gauge. These points are illustrated explicitly with the one-loop calculations of the effective action. With a field redefinition, we obtain the physical effective potential. The SU(2) non-Abelian case is also discussed.

scholarly journals Extensions of associative algebras

2014 ◽  
Vol 16 (03) ◽  
pp. 1450014
Author(s):  
Alice Fialowski ◽  
Michael Penkava
Keyword(s):  
Associative Algebra ◽  
Moduli Spaces ◽  
Associative Algebras ◽  
Versal Deformations ◽  
Low Dimensional

In this paper, we translate the problem of extending an associative algebra by another associative algebra into the language of codifferentials. The authors have been constructing moduli spaces of algebras and studying their structure by constructing their versal deformations. The codifferential language is very useful for this purpose. The goal of this paper is to express the classical results about extensions in a form which leads to a simpler construction of moduli spaces of low-dimensional algebras.

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