Please use this identifier to cite or link to this item:
http://doi.org/10.25358/openscience-1028
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 |
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