Castelnuovo-Mumford regularity of ladder determinantal varieties and patches of Grassmannian Schubert varieties
نویسندگان
چکیده
We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and 1432-avoiding via tableau combinatorics. These generalize a formula degrees of symmetric which appeared in previous joint work the authors with Y. Ren A. St. Dizier. apply our to compute Castelnuovo-Mumford regularity classes generalized determinantal ideals. In particular, we combinatorial regularities all one-sided mixed ladder also derive certain Kazhdan-Lusztig ideals, including those coming from open patches Schubert varieties Grassmannians. This provides correction conjecture Kummini-Lakshmibai-Sastry-Seshadri (2015).
منابع مشابه
Hilbert functions of ladder determinantal varieties
We consider algebraic varieties de)ned by the vanishing of all minors of a )xed size of a rectangular matrix with indeterminate entries such that the indeterminates in these minors are restricted to lie in a ladder shaped region of the rectangular array. Explicit formulae for the Hilbert function of such varieties are obtained in (i) the rectangular case by Abhyankar (Rend. Sem. Mat. Univers. P...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2023
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2022.11.001