An algebraic approach to finite projective planes

David Cook, Juan Migliore, Uwe Nagel, Fabrizio Zanello

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley–Reisner ring (Formula presented.) and the inverse system algebra (Formula presented.). We give a careful study of both of these algebras. Our main results are a full description of the graded Betti numbers of both algebras in the more general setting of linear spaces (giving the result for the projective planes as a special case), and a classification of the characteristics in which the inverse system algebra associated to a finite projective plane has the weak or strong Lefschetz Property.

Original languageEnglish
Pages (from-to)495-519
Number of pages25
JournalJournal of Algebraic Combinatorics
Volume43
Issue number3
DOIs
StatePublished - May 1 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media New York.

Keywords

  • Finite projective plane
  • Inverse system
  • Level algebra
  • Linear space
  • Minimal free resolution
  • Monomial algebra
  • Stanley–Reisner ring
  • Strong Lefschetz property
  • Weak Lefschetz property

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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