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 language | English |
|---|---|
| Pages (from-to) | 495-519 |
| Number of pages | 25 |
| Journal | Journal of Algebraic Combinatorics |
| Volume | 43 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 1 2016 |
Bibliographical note
Funding Information: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).
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