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Moduli spaces of varieties with symmetries

URN to cite this document: urn:nbn:de:bvb:703-epub-2970-4

Title data

Li, Binru:
Moduli spaces of varieties with symmetries.
Bayreuth , 2016 . - 72 P.
( Doctoral thesis, 2016 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

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Project information

Project financing: ERC Advanced Grant

Abstract

In this thesis several topics on moduli problems of varieties with symmetries are treated. We show the existence of the coarse moduli scheme $\mathfrak{M}_h[G]$ for Gorenstein canonical models with Hilbert polynomial $h$ which admit an effective action by a given finite group $G$. We also introduce a canonical representation type decomposition $\mathcal{D}_h[G]$ of $\mathfrak{M}_h[G]$ which is useful in understanding the structure of $\mathfrak{M}_h[G]$. We explain the method to determine the irreducible components of $\mathfrak{M}_g(G)$, the locus inside $\mathfrak{M}_g$ of smooth curves with an effective action by a finite group $G$. We do explicit computations for the cases where $G$ is a cyclic or dihedral group.

Abstract in another language

In dieser Arbeit werden verschiedene Themen von Modulraumproblemen von Varietäten mit Symmetrien behandelt. Wir zeigen die Existenz des groben Modulraum-Schemas $\mathfrak{M}_h[G]$ für kanonische Gorensteinmodelle mit Hilbertpolynom $h$, die eine effektive Gruppenoperation einer gegebenen endlichen Gruppe $G$ besitzen. Desweiteren führen wir eine kanonische Zerlegung nach dem Darstellungstyp $\mathcal{D}_h[G]$ von $\mathfrak{M}_h[G]$ ein, die sehr nützlich für das Verständnis der Struktur von $\mathfrak{M}_h[G]$. Wir beschreiben die Methode, die irreduziblen Komponenten von $\mathfrak{M}_g(G)$ (dem Ort der glatten Kurven in $\mathfrak{M}_g$ mit einer effektiven Operation einer endlichen Gruppe $G$) zu finden. In den Fällen wo $G$ zyklisch oder eine Diedergruppe ist, wird diese Methode zusammen mit expliziten Berechnungen angewandt.

Further data

Item Type: Doctoral thesis (No information)
Keywords: Coarse moduli space; G-marked variety; Gorenstein canonical model; Moduli of curves
Subject classification: MSC: 14C05, 14D22, 14H10, 14H15, 14H30, 14J10, 32G15
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VIII (Algebraic Geometry)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors > Chair Mathematics VIII (Algebraic Geometry) - Univ.-Prof. Dr. Fabrizio Catanese
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-2970-4
Date Deposited: 19 Aug 2016 07:06
Last Modified: 19 Aug 2016 08:09
URI: https://epub.uni-bayreuth.de/id/eprint/2970

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