4 citations · 8 across the 8 of their papers we have counts for
6 papers · 1 filter
Gröbner geometry for regular nilpotent Hessenberg Schubert cells
Mike Cummings, Sergio Da Silva, Megumi Harada +1
A regular nilpotent Hessenberg Schubert cell is the intersection of a regular nilpotent Hessenberg variety with a Schubert cell. In this paper, we describe a set of minimal generat…
Geometric vertex decomposition, Gröbner bases, and Frobenius splittings for regular nilpotent Hessenberg varieties
Sergio Da Silva, Megumi Harada
We initiate a study of the Gröbner geometry of local defining ideals of Hessenberg varieties by studying the special case of regular nilpotent Hessenberg varieties in Lie type A, a…
Degenerations of Pascal Lines
Jaydeep Chipalkatti, Sergio Da Silva
Let denote a nonsingular conic in the complex projective plane. Pascal's theorem says that, given six distinct points on , the three inters…
Strict Bott-Samelson Resolutions of Schubert Varieties
Sergio Da Silva
We explore the relationship between two desingularization techniques for Schubert varieties. The Bott-Samelson resolution is the more common of the two, but it fails to encompass m…
Desingularization by blowings-up avoiding simple normal crossings
Edward Bierstone, Sergio Da Silva, Pierre D. Milman +1
It is shown that, for any reduced algebraic variety in characteristic zero, one can resolve all but simple normal crossings (snc) singularities by a finite sequence of blowings-up…
On Oda's Strong Factorization Conjecture
Sergio Da Silva, Kalle Karu
The Oda's Strong Factorization Conjecture states that a proper birational map between smooth toric varieties can be decomposed as a sequence of smooth toric blowups followed by a s…