Hilbert Function and Dimension

2002 ◽  
pp. 275-312
Author(s):  
Gert-Martin Greuel ◽  
Gerhard Pfister
Keyword(s):  
Hilbert Function

Intersection theory and Hilbert function

2011 ◽  
Vol 45 (4) ◽  
pp. 305-315
Author(s):  
A. G. Khovanskii
Keyword(s):  
Hilbert Function ◽  
Intersection Theory

scholarly journals Hilbert function of local Artinian level rings in codimension two

2009 ◽  
Vol 321 (5) ◽  
pp. 1429-1442 ◽  
Author(s):  
Valentina Bertella
Keyword(s):  
Hilbert Function ◽  
Codimension Two

scholarly journals Stanley’s conjecture for critical ideals

2011 ◽  
Vol 48 (2) ◽  
pp. 220-226
Author(s):  
Azeem Haider ◽  
Sardar Khan
Keyword(s):  
Polynomial Ring ◽  
Hilbert Function ◽  
Monomial Ideal ◽  
Monomial Ideals ◽  
Stanley Depth

Let S = K[x1,…,xn] be a polynomial ring in n variables over a field K. Stanley’s conjecture holds for the modules I and S/I, when I ⊂ S is a critical monomial ideal. We calculate the Stanley depth of S/I when I is a canonical critical monomial ideal. For non-critical monomial ideals we show the existence of a Stanley ideal with the same depth and Hilbert function.

scholarly journals Bundles on with vanishing lower cohomologies

2020 ◽  
pp. 1-20
Author(s):  
Mengyuan Zhang
Keyword(s):  
Hilbert Function ◽  
Betti Numbers ◽  
Projective Spaces ◽  
Hilbert Functions ◽  
Free Resolutions ◽  
Rational Varieties ◽  
Minimal Free Resolutions ◽  
Graded Lattice

Abstract We study bundles on projective spaces that have vanishing lower cohomologies using their short minimal free resolutions. We partition the moduli $\mathcal{M}$ according to the Hilbert function H and classify all possible Hilbert functions H of such bundles. For each H, we describe a stratification of $\mathcal{M}_H$ by quotients of rational varieties. We show that the closed strata form a graded lattice given by the Betti numbers.

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