Algorithms for singularities and real structures of weak Del Pezzo surfaces

Niels Lubbes

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)1350158
JournalJournal of Algebra and Its Applications
Volume13
Issue number05
DOIs
StatePublished - Aug 2014

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Algorithms for singularities and real structures of weak Del Pezzo surfaces'. Together they form a unique fingerprint.

Cite this