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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/100/1773

Title: Hilbert functions of ladder determinantal varieties
Authors: GHORPADE, SR
Keywords: schubert varieties
pfaffian ideals
lattice paths
rings
normality
singularities
formula
loci
Issue Date: 2002
Publisher: ELSEVIER SCIENCE BV
Citation: DISCRETE MATHEMATICS,246,131-175
Abstract: We consider algebraic varieties defined by the vanishing of all minors of a fixed 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. Politecn. Torino 42 (1984) 65), and (ii) the case of 2 x 2 minors in one-sided ladders by Kulkami (Semigroup of ordinary multiple point, analysis of straightening formula and counting monomials, Ph.D. Thesis, Purdue University, West Lafayette, USA, 1985). More recently, Krattenthaler and Prohaska (Trans. Amer. Math. Soc. 351 (1999) 1015) have proved a,remarkable formula', conjectured by Conca and Herzog (Adv. Math. 132 (1997) 120) for the Hilbert series in the case of arbitrary sized minors in one-sided ladders. We describe here an explicit, albeit complicated, formula for the Hilbert function and the Hilbert series in the case of arbitrary sized minors in two-sided ladders. From a combinatorial viewpoint, this is equivalent to the enumeration of certain sets of 'indexed monomials'. (C) 2002 Elsevier Science B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/S0012-365X(01)00256-4
http://dspace.library.iitb.ac.in/xmlui/handle/10054/15015
http://hdl.handle.net/100/1773
ISSN: 0012-365X
Appears in Collections:Proceedings papers

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