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Classification and Moduli Spaces of Surfaces of General Type with Pg = q =1

URN to cite this document: urn:nbn:de:bvb:703-epub-3356-3

Title data

Ling, Songbo:
Classification and Moduli Spaces of Surfaces of General Type with Pg = q =1.
Bayreuth , 2017 . - 53 P.
( Doctoral thesis, 2017 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

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Project's official titleProject's id
Chinese Government Graduate Student Overseas Study ProgramNo information

Project financing: Chinese Scholarship Council

Abstract

This thesis is devoted to the classification and moduli spaces of surfaces of general type with Pg = q = 1. First we consider the case g = 2, K² = 5 (where g is the genus of the Albanese fibre) and prove that the surfaces constructed by Catanese [10] Example 8) constitute a connected component of the moduli space of surfaces with Pg = q = 1, K² = 5. Then we consider the case g = 3, K² = 4 and give two irreducible components of the moduli space of surfaces with Pg = q = 1, K² = 4. Finally, we prove that the number of direct summands of the direct image of the bicanonical sheaf under the Albanese map is not a deformation invariant, which gives a negative answer to Pignatelli's question [35].

Abstract in another language

Die vorliegende Dissertation beschäftigt sich mit der Klassifikation von Flächen allgemeinen Typs mit Pg = q = 1 und deren Modulräuumen. Zunächst betrachten wir den Fall g = 2, K² = 5 (wobei g das Geschlecht der Albanesefaser bezeichne) und zeigen, dass die von Catanese in [10], Example 8 konstruierten Flächen eine Zusammenhangskomponente des Modulraums der Flächen von allgemeinem Typ mit Pg = q = 1 und K² = 5 bilden. Danach wird der Fall g = 3, K² = 4 untersucht; hierbei geben wir zwei irreduzible Komponenten des Modulraums der Flächen von allgemeinem Typ mit Pg = q = 1 und K² = 4 an. Am Ende geben wir eine negative Antwort auf eine Frage von Pignatelli in [35], indem wir zeigen, dass die Anzahl der direkten Summanden des direkten Bildes der bikanonischen Garbe unter der Albaneseabbildung nicht invariant unter Deformationen ist.

Further data

Item Type: Doctoral thesis (No information)
Keywords: surfaces of general type; Pg =q = 1; moduli space
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: 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
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
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3356-3
Date Deposited: 01 Aug 2017 12:06
Last Modified: 01 Aug 2017 12:06
URI: https://epub.uni-bayreuth.de/id/eprint/3356

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