The Curvature of the Petersson-Weil Metric on the Moduli Space of Kähler-Einstein Manifolds

1993 ◽  
pp. 339-354 ◽  
Author(s):  
Georg Schumacher
Keyword(s):  
Moduli Space ◽  
Einstein Manifolds

scholarly journals MODULI SPACE OF TOPOLOGICAL TWO-FORM GRAVITY

1994 ◽  
Vol 09 (10) ◽  
pp. 895-901 ◽  
Author(s):  
MITSUKO ABE ◽  
AKIKA NAKAMICHI ◽  
TATSUYA UENO
Keyword(s):  
Cosmological Constant ◽  
Moduli Space ◽  
Einstein Gravity ◽  
Einstein Manifolds ◽  
Topological Version ◽  
Elliptic Complex

We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual two-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual Einstein manifolds. In the presence of a cosmological constant, we evaluate the index of the elliptic complex associated with the moduli space.

Topology of the quantum modified moduli space

2001 ◽  
Vol 15 (4) ◽  
pp. 279-289
Author(s):  
S. L. Dubovsky
Keyword(s):  
Moduli Space

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Quasi-projectivity of the moduli space of smooth Kähler-Einstein Fano manifolds

2018 ◽  
Vol 51 (3) ◽  
pp. 739-772 ◽  
Author(s):  
Chi Li ◽  
Xiaowei Wang ◽  
Chenyang Xu
Keyword(s):  
Moduli Space ◽  
Fano Manifolds

Brown's dihedral moduli space and freedom of the gravity operad

2017 ◽  
Vol 50 (5) ◽  
pp. 1081-1122 ◽  
Author(s):  
Johan Alm ◽  
Dan Petersen
Keyword(s):  
Moduli Space

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 Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anthony Ashmore ◽  
Sebastian Dumitru ◽  
Burt A. Ovrut
Keyword(s):  
Line Bundle ◽  
Supersymmetry Breaking ◽  
Moduli Space ◽  
Initial Conditions ◽  
Low Energy ◽  
Strongly Coupled ◽  
Hidden Sector ◽  
Effective Lagrangian ◽  
Soft Supersymmetry Breaking ◽  
M Theory

Abstract The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

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