An algebraic approach to finite projective planes
Document Type
Article
Publication Date
5-2016
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 R/IΛ and the inverse system algebra R/IΔ . 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.
Publication Title
Journal of Algebraic Combinatorics
Recommended Citation
Cook, D.,
Migliore, J.,
Nagel, U.,
&
Zanello, F.
(2016).
An algebraic approach to finite projective planes.
Journal of Algebraic Combinatorics,
43(3), 495-519.
http://doi.org/10.1007/s10801-015-0644-8
Retrieved from: https://digitalcommons.mtu.edu/math-fp/59
Publisher's Statement
© Springer Science+Business Media New York 2015. Publisher’s version of record: https://dx.doi.org/10.1007/s10801-015-0644-8