Authors:	Samol, Sonia
Title:	Effective bounds for the negativity of Shimura curves on Hilbert modular surfaces
Online publication date:	6-Oct-2016
Year of first publication:	2016
Language:	english
Abstract:	The Bounded Negativity Conjecture states that for each smooth projective surface X defined over a field of characteristic zero there exists a number b(X) bigger or equal to 0 such that the self-intersection number C^2 for every reduced, irreducible curve C in X is bounded below by b(X), i.e. C^2 is bigger or equal to -b(X). In this thesis, we consider Hirzebruch-Zagier curves on Hilbert modular surfaces and give explicit bounds for the self-intersection numbers in these cases. More general, we give a bound for the self-intersection number of reduced, irreducible Shimura curves C on Hilbert modular surfaces X, generalising a result from the literature from compact Hilbert modular surfaces to non-compact Hilbert modular surfaces. We compare the resulting bounds with the actual self-intersection numbers of Hirzebruch-Zagier curves calculated with Pari/GP.
DDC:	510 Mathematik 510 Mathematics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-1028
URN:	urn:nbn:de:hebis:77-diss-1000007063
Version:	Original work
Publication type:	Dissertation
License:	In Copyright
Information on rights of use:	https://rightsstatements.org/vocab/InC/1.0/
Extent:	viii, 82 Seiten
Appears in collections:	JGU-Publikationen