scholarly journals The moduli space of Hessian quartic surfaces and automorphic forms

2012 ◽  
Vol 216 (10) ◽  
pp. 2233-2240 ◽  
Author(s):  
Shigeyuki Kondō
Keyword(s):  
Moduli Space ◽  
Automorphic Forms ◽  
Quartic Surfaces

scholarly journals K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space IV: The structure of the invariant

2020 ◽  
Vol 156 (10) ◽  
pp. 1965-2019
Author(s):  
Shouhei Ma ◽  
Ken-Ichi Yoshikawa
Keyword(s):  
Modular Form ◽  
Moduli Space ◽  
Automorphic Forms ◽  
K3 Surfaces ◽  
Automorphic Function ◽  
Siegel Modular Form ◽  
Analytic Torsion ◽  
Invent Math ◽  
Torsion Invariant

AbstractYoshikawa in [Invent. Math. 156 (2004), 53–117] introduces a holomorphic torsion invariant of $K3$ surfaces with involution. In this paper we completely determine its structure as an automorphic function on the moduli space of such $K3$ surfaces. On every component of the moduli space, it is expressed as the product of an explicit Borcherds lift and a classical Siegel modular form. We also introduce its twisted version. We prove its modularity and a certain uniqueness of the modular form corresponding to the twisted holomorphic torsion invariant. This is used to study an equivariant analogue of Borcherds’ conjecture.

scholarly journals A LINEAR SYSTEM ON NARUKI'S MODULI SPACE OF MARKED CUBIC SURFACES

2002 ◽  
Vol 13 (02) ◽  
pp. 183-208 ◽  
Author(s):  
BERT VAN GEEMEN
Keyword(s):  
Linear System ◽  
Projective Space ◽  
Weyl Group ◽  
Root System ◽  
Moduli Space ◽  
Automorphic Forms ◽  
Cubic Surfaces ◽  
Ball Quotients ◽  
Dimensional Projective Space

Allcock and Freitag recently showed that the moduli space of marked cubic surfaces is a subvariety of a nine dimensional projective space which is defined by cubic equations. They used the theory of automorphic forms on ball quotients to obtain these results. Here we describe the same embedding using Naruki's toric model of the moduli space. We also give an explicit parametrization of the tritangent divisors, we discuss another way to find equations for the image and we show that the moduli space maps, with degree at least ten, onto the unique quintic hypersurface in a five dimensional projective space which is invariant under the action of the Weyl group of the root system E6.

scholarly journals On augmented Schottky spaces and automorphic forms, I

1979 ◽  
Vol 75 ◽  
pp. 151-175 ◽  
Author(s):  
Hiroki Sato
Keyword(s):  
Moduli Space ◽  
Riemann Surfaces ◽  
Automorphic Forms ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces

With respect to Teichmüller spaces, many beautiful results are obtained by TeichmüUer, Ahlfors, Bers, Maskit, Kra, Earle, Abikoff, and others. For example, the boundary consists of b-groups, and the augmented Teichmüller space is defined by attaching a part of the boundary to the Teichmüller space. By using the augmented Teichmüller space, a compactification of the moduli space of Riemann surfaces is accomplished (cf. Abikoff [1], Bers [2]).

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.

Sign in / Sign up

Export Citation Format

Share Document