Algebraic curves hermitian lattices and hypergeometric functions

Download

index.pdf

Date

2011

Author

Zeytin, Ayberk

Metadata

Show full item record

Item Usage Stats

281
views

114
downloads

The aim of this work is to study the interaction between two classical objects of mathematics: the modular group, and the absolute Galois group. The latter acts on the category of finite index subgroups of the modular group. However, it is a task out of reach do understand this action in this generality. We propose a lattice which parametrizes a certain system of ”geometric” elements in this category. This system is setwise invariant under the Galois action, and there is a hope that one can explicitly understand the pointwise action on the elements of this system. These elements admit moreover a combinatorial description as quadrangulations of the sphere, satisfying a natural nonnegative curvature condition. Furthermore, their connections with hypergeometric functions allow us to realize these quadrangulations as points in the moduli space of rational curves with 8 punctures. These points are conjecturally defined over a number field and our ultimate wish is to compare the Galois action on the lattice elements in the category and the corresponding points in the moduli space.

Subject Keywords

Geometry, Algebraic., Linear algebraic groups., Group theory.

URI

http://etd.lib.metu.edu.tr/upload/12613485/index.pdf
https://hdl.handle.net/11511/20747

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Equivariant Picard groups of the moduli spaces of some finite Abelian covers of the Riemann sphere Ozan, Yıldıray (2023-03-01) In this note, following Kordek's work we will compute the equivariant Picard groups of the moduli spaces of Riemann surfaces with certain finite abelian symmetries.
Universal groups of intermediate growth and their invariant random subgroups Benli, Mustafa Gökhan; Nagnibeda, Tatiana (2015-07-01) We exhibit examples of groups of intermediate growth with ergodic continuous invariant random subgroups. The examples are the universal groups associated with a family of groups of intermediate growth.
Descriptive complexity of subsets of the space of finitely generated groups Benli, Mustafa Gökhan; Kaya, Burak (2022-12-01) © 2022 Elsevier GmbHIn this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish that the sets of solvable groups, groups of exponential growth and groups with decidable word problem are Σ20-complete and that the sets of periodic groups and groups of intermediate growth are Π20-complete. We also provide bounds for the descriptive complexity of simplicity, amenability,...
Knotting of algebraic curves in CP2 Finashin, Sergey (2002-01-01) For any k⩾3, I construct infinitely many pairwise smoothly non-isotopic smooth surfaces homeomorphic to a non-singular algebraic curve of degree 2k, realizing the same homology class as such a curve and having abelian fundamental group ⧹ . This gives an answer to Problem 4.110 in the Kirby list (Kirby, Problems in low-dimensional topology, in: W. Kazez (Ed.), Geometric Topology, AMS/IP Stud. Adv. Math. vol 2.2, Amer. Math. Soc., Providence, 1997).
Finite groups having nonnormal TI subgroups Kızmaz, Muhammet Yasir (2018-08-01) In the present paper, the structure of a finite group G having a nonnormal T.I. subgroup H which is also a Hall pi-subgroup is studied. As a generalization of a result due to Gow, we prove that H is a Frobenius complement whenever G is pi-separable. This is achieved by obtaining the fact that Hall T.I. subgroups are conjugate in a finite group. We also prove two theorems about normal complements one of which generalizes a classical result of Frobenius.

Citation Formats

A. Zeytin, “Algebraic curves hermitian lattices and hypergeometric functions,” Ph.D. - Doctoral Program, Middle East Technical University, 2011.