Addendum to ”frobenius and Cartier Algebras of Stanley-reisner

On Isomorphism of Simplicial Complexes and Their Related Algebras

On a special class of Stanley-Reisner ideals

For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...

On Toric Face Rings

Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley–Reisner and affine monoid algebras. The main goal of this article is to unify parts of the theories of Stanley–Reisnerand affine monoid algebras. We consider (nonpure) shellable fan’s and the Cohen–Macaulay property. More...

Schubert Varieties, Subword Complexes, Frobenius Splitting, and Bruhat Atlases

We consider stratifications of schemes by subvarieties, and introduce the notion of a stratification generated by a collection of (reduced) subschemes. We recall some basics of Gröbner degenerations (just for lex order) and Stanley-Reisner theory. We then state the main theorem, that the lex init of a Kazhdan-Lusztig variety in BottSamelson coördinates is the Stanley-Reisner scheme of a subword...

K2 Factors of Koszul Algebras and Applications to Face Rings

Generalizing the notion of a Koszul algebra, a graded kalgebra A is K2 if its Yoneda algebra ExtA(k, k) is generated as an algebra in cohomology degrees 1 and 2. We prove a strong theorem about K2 factor algebras of Koszul algebras and use that theorem to show the Stanley-Reisner face ring of a simplicial complex ∆ is K2 whenever the Alexander dual simplicial complex ∆∗ is (sequentially) Cohen-...