31 citations · 262 across the 48 of their papers we have counts for
50 papers
The minimal free resolution of a generic symmetric principal ideal
Megumi Harada, Alexandra Seceleanu, Liana Şega
We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of t…
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…
The cohomology rings of regular nilpotent Hessenberg varieties
Megumi Harada, Tatsuya Horiguchi
This manuscript is a contributed chapter in the forthcoming CRC Press volume, titled the Handbook of Combinatorial Algebraic Geometry: Subvarieties of the Flag Variety. The book, a…
Hadamard Products and Binomial Ideals
Büşra Atar, Kieran Bhaskara, Adrian Cook +6
We study the Hadamard product of two varieties and , with particular attention to the situation when one or both of and is a binomial variety. The main result of thi…
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…
Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties
Megumi Harada, Martha Precup
It is well-known that the -fixed points of a Schubert variety in the flag variety can be characterized purely combinatorially in terms of Bruhat order on th…