A Grobner Basis for Schubert Patch Ideals
Speaker:
Emmanuel Neye, University of Saskatchewan
Date and Time:
Friday, January 21, 2022 - 4:20pm to 4:40pm
Location:
online
Abstract:
Schubert patch ideals are a class of generalized determinantal ideals. They are prime defining ideals of open patches of Schubert varieties in the type A flag variety. In this talk, E. Gorla, J. Migliore, and U. Nagel’s “Grobner basis via linkage” technique will be adapted to prove a conjecture of A. Yong, namely, the essential minors of every Schubert patch ideal form a Grobner basis. Using the same approach, the result of A. Woo and A. Yong that the essential minors of a Kazhdan-Lusztig ideal form a Grobner basis will be recovered. With respect to standard grading, it will be shown that the homogeneous Schubert patch ideals and homogeneous Kazhdan-Lusztig ideals (and hence, the Schubert determinantal ideals) are glicci.