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dc.contributor.authorLubbes, Niels
dc.date.accessioned2015-08-03T12:05:28Z
dc.date.available2015-08-03T12:05:28Z
dc.date.issued2014-02-25
dc.identifier.citationLUBBES, N. (2014). ALGORITHMS FOR SINGULARITIES AND REAL STRUCTURES OF WEAK DEL PEZZO SURFACES. Journal of Algebra and Its Applications, 13(05), 1350158. doi:10.1142/s0219498813501582
dc.identifier.issn0219-4988
dc.identifier.issn1793-6829
dc.identifier.doi10.1142/S0219498813501582
dc.identifier.urihttp://hdl.handle.net/10754/563664
dc.description.abstract<jats:p> 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. </jats:p>
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.
dc.publisherWorld Scientific Pub Co Pte Lt
dc.relation.urlhttps://www.worldscientific.com/doi/abs/10.1142/S0219498813501582
dc.relation.urlhttp://arxiv.org/pdf/1302.6678
dc.rightsElectronic version of an article published as [[JournalTitle], 13, 05, 2014] DOI:10.1142/S0219498813501582 © [copyright World Scientific Publishing Company]
dc.rightsThis file is an open access version redistributed from: http://arxiv.org/pdf/1302.6678
dc.subjectCyclides
dc.subjectReal structure
dc.subjectRoot systems
dc.subjectSingularities
dc.subjectWeak Del Pezzo surface
dc.titleAlgorithms for singularities and real structures of weak Del Pezzo surfaces
dc.typeArticle
dc.contributor.departmentComputer Science Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.identifier.journalJournal of Algebra and Its Applications
dc.identifier.wosutWOS:000332117600014
dc.eprint.versionPre-print
dc.identifier.volume13
dc.identifier.issue05
dc.identifier.pages1350158
dc.identifier.arxivid1302.6678
kaust.personLubbes, Niels
dc.identifier.eid2-s2.0-84897662844
refterms.dateFOA2021-04-28T10:07:52Z
dc.date.posted2013-02-27


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