Geodesic
An algebraic approach to finite projective planes
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 3, pp. 495-519.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $R/I_\Lambda $ and the inverse system algebra $R/I_\Delta $. 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.
Classification : 05E40, 05B25, 13D02, 13E10, 13H10, 51E15
Keywords: finite projective plane, linear space, weak Lefschetz property, strong Lefschetz property, minimal free resolution, monomial algebra, level algebra, Stanley-Reisner ring, inverse system 
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     title = {An algebraic approach to finite projective planes},
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Cook, David II; Migliore, Juan; Nagel, Uwe; Zanello, Fabrizio. An algebraic approach to finite projective planes. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 3, pp. 495-519. http://geodesic.mathdoc.fr/item/JAC_2016__43_3_a8/