Hilbert functions of ladder determinantal varieties
type: Item
instance of: scholarly article
title: Hilbert functions of ladder determinantal varieties
zbMATH Open document ID: 1008.14011
DOI: 10.1016/S0012-365X(01)00256-4
author: Sudhir R. Ghorpade
published in: Discrete Mathematics
publication date: 2002-05-15T00:00:00Z
review text: In the paper under review the author studies algebraic varieties defined by minors of a fixed size of a matrix such that all minors are restricted to lie in a ladder shaped region. The main result are explicit formulas for the Hilbert functions and Hilbert series related to these varieties. In particular, the author shows that, although the formulas in the general case are complicated, they can be used to derive fairly simple estimates for some useful geometric invariants of the varieties such as the degree of the Hilbert polynomial.
reviewed by: Vesselin Drensky
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 13C40
zbMATH DE Number: 1741706
zbMATH Keywords: determinantal ideals
zbMATH Keywords: Hilbert functions
zbMATH Keywords: determinantal varieties
zbMATH Keywords: Schubert varieties
zbMATH Keywords: ladder determinantal varieties
zbMATH Keywords: Hilbert series
MaRDI profile type: Publication
Recommended article: Q3735861
Recommended article: Hilbert polynomial of a certain ladder-determinantal ideal
Recommended article: Mixed ladder determinantal varieties
Recommended article: The hilbert function of some reducible varieties
Recommended article: Q4444129
Recommended article: Q3369810
Recommended article: Graded Multiplicity Theory and Hilbert Functions
Recommended article: Hilbert series of certain jet schemes of determinantal varieties
Recommended article: The irreducibility of ladder determinantal varieties
Recommended article: Hilbert functions and level algebras
description: scientific article; zbMATH DE number 1741706