Algorithms for singularities and real structures of weak Del Pezzo surfaces

Handle URI:
http://hdl.handle.net/10754/563664
Title:
Algorithms for singularities and real structures of weak Del Pezzo surfaces
Authors:
Lubbes, Niels
Abstract:
In this paper, we consider the classification of singularities [P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction. I, II, III, Proc. Camb. Philos. Soc. 30 (1934) 453-491] and real structures [C. T. C. Wall, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math. 1987(375/376) (1987) 47-66, ISSN 0075-4102] of weak Del Pezzo surfaces from an algorithmic point of view. It is well-known that the singularities of weak Del Pezzo surfaces correspond to root subsystems. We present an algorithm which computes the classification of these root subsystems. We represent equivalence classes of root subsystems by unique labels. These labels allow us to construct examples of weak Del Pezzo surfaces with the corresponding singularity configuration. Equivalence classes of real structures of weak Del Pezzo surfaces are also represented by root subsystems. We present an algorithm which computes the classification of real structures. This leads to an alternative proof of the known classification for Del Pezzo surfaces and extends this classification to singular weak Del Pezzo surfaces. As an application we classify families of real conics on cyclides. © World Scientific Publishing Company.
KAUST Department:
Computer Science Program
Publisher:
World Scientific Pub Co Pte Lt
Journal:
Journal of Algebra and Its Applications
Issue Date:
Aug-2014
DOI:
10.1142/S0219498813501582
ARXIV:
arXiv:1302.6678
Type:
Article
ISSN:
02194988
Sponsors:
It is my pleasure to acknowledge that the many computations with Josef Schicho is a major contribution to this paper. Also he recognized the Pappus configuration of Example 7. I would like to thank Michael Harrison for useful discussions concerning root subsystems. I would like to thank Ulrich Derenthal for informing me of a mistake in a previous version of this paper. The algorithms were implemented using the computer algebra system Sage ([18]). This research was supported by the Austrian Science Fund (FWF): project P21461.
Additional Links:
http://arxiv.org/abs/arXiv:1302.6678v5
Appears in Collections:
Articles; Computer Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorLubbes, Nielsen
dc.date.accessioned2015-08-03T12:05:28Zen
dc.date.available2015-08-03T12:05:28Zen
dc.date.issued2014-08en
dc.identifier.issn02194988en
dc.identifier.doi10.1142/S0219498813501582en
dc.identifier.urihttp://hdl.handle.net/10754/563664en
dc.description.abstractIn this paper, we consider the classification of singularities [P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction. I, II, III, Proc. Camb. Philos. Soc. 30 (1934) 453-491] and real structures [C. T. C. Wall, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math. 1987(375/376) (1987) 47-66, ISSN 0075-4102] of weak Del Pezzo surfaces from an algorithmic point of view. It is well-known that the singularities of weak Del Pezzo surfaces correspond to root subsystems. We present an algorithm which computes the classification of these root subsystems. We represent equivalence classes of root subsystems by unique labels. These labels allow us to construct examples of weak Del Pezzo surfaces with the corresponding singularity configuration. Equivalence classes of real structures of weak Del Pezzo surfaces are also represented by root subsystems. We present an algorithm which computes the classification of real structures. This leads to an alternative proof of the known classification for Del Pezzo surfaces and extends this classification to singular weak Del Pezzo surfaces. As an application we classify families of real conics on cyclides. © World Scientific Publishing Company.en
dc.description.sponsorshipIt is my pleasure to acknowledge that the many computations with Josef Schicho is a major contribution to this paper. Also he recognized the Pappus configuration of Example 7. I would like to thank Michael Harrison for useful discussions concerning root subsystems. I would like to thank Ulrich Derenthal for informing me of a mistake in a previous version of this paper. The algorithms were implemented using the computer algebra system Sage ([18]). This research was supported by the Austrian Science Fund (FWF): project P21461.en
dc.publisherWorld Scientific Pub Co Pte Lten
dc.relation.urlhttp://arxiv.org/abs/arXiv:1302.6678v5en
dc.subjectCyclidesen
dc.subjectReal structureen
dc.subjectRoot systemsen
dc.subjectSingularitiesen
dc.subjectWeak Del Pezzo surfaceen
dc.titleAlgorithms for singularities and real structures of weak Del Pezzo surfacesen
dc.typeArticleen
dc.contributor.departmentComputer Science Programen
dc.identifier.journalJournal of Algebra and Its Applicationsen
dc.identifier.arxividarXiv:1302.6678en
kaust.authorLubbes, Nielsen
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