An algebraic approach to finite projective planes

David Cook; Juan Migliore; Uwe Nagel; Fabrizio Zanello

doi:10.1007/s10801-015-0644-8

An algebraic approach to finite projective planes

David Cook
, Juan Migliore
, Uwe Nagel
, Fabrizio Zanello

Mathematics

Producción científica: Article › revisión exhaustiva

3 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	495-519
Número de páginas	25
Publicación	Journal of Algebraic Combinatorics
Volumen	43
N.º	3
DOI	https://doi.org/10.1007/s10801-015-0644-8
Estado	Published - may 1 2016

Nota bibliográfica

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

Financiación

The work for this paper was done while J. Migliore was partially supported by the National Security Agency under Grant Number H98230-12-1-0204 and by a Simons Foundation grant (#309556), while U. Nagel was partially supported by the National Security Agency under Grant Number H98230-12-1-0247 and by the Simons Foundation under Grant #317096, and while F. Zanello was partially supported by a Simons Foundation Grant (#274577).

Financiadores	Número del financiador
Simons Foundation	274577, 317096, 309556, H98230-12-1-0247
National Security Agency	H98230-12-1-0204

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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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.",

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AU - Nagel, Uwe

AU - Zanello, Fabrizio

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AB - 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.

KW - Finite projective plane

KW - Inverse system

KW - Level algebra

KW - Linear space

KW - Minimal free resolution

KW - Monomial algebra

KW - Stanley–Reisner ring

KW - Strong Lefschetz property

KW - Weak Lefschetz property

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An algebraic approach to finite projective planes

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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