Hilbert functions and Betti numbers of homogeneous ideals in an exterior algebra

2004 ◽  
Vol 59 (5) ◽  
pp. 976-978 ◽  
Author(s):  
D A Shakin
Keyword(s):  
Betti Numbers ◽  
Exterior Algebra ◽  
Hilbert Functions ◽  
Homogeneous Ideals

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.

Hilbert functions and Betti numbers in a flat family

1985 ◽  
Vol 142 (1) ◽  
pp. 277-292 ◽  
Author(s):  
M. Boratyński ◽  
S. Greco
Keyword(s):  
Betti Numbers ◽  
Hilbert Functions ◽  
Flat Family

ON THE DEGREES OF MINIMAL GENERATORS OF HOMOGENEOUS IDEALS IN THE EXTERIOR ALGEBRA

2001 ◽  
Vol 29 (11) ◽  
pp. 5155-5170 ◽  
Author(s):  
Guillermo Moreno-Socías ◽  
Jan Snellman
Keyword(s):  
Exterior Algebra ◽  
Minimal Generators ◽  
Homogeneous Ideals

Lyubeznik and Betti numbers for homogeneous ideals

2020 ◽  
Vol 50 (6) ◽  
pp. 2157-2165
Author(s):  
Parvaneh Nadi ◽  
Farhad Rahmati
Keyword(s):  
Betti Numbers ◽  
Homogeneous Ideals

scholarly journals Rigidity of Linear Strands and Generic Initial Ideals

2008 ◽  
Vol 190 ◽  
pp. 35-61 ◽  
Author(s):  
Satoshi Murai ◽  
Pooja Singla
Keyword(s):  
Polynomial Ring ◽  
Betti Numbers ◽  
Exterior Algebra ◽  
Graded Betti Numbers ◽  
Linear Resolution ◽  
Initial Ideals ◽  
Finite Set ◽  
Generic Initial Ideals ◽  
The Ideal

Let K be a field, S a polynomial ring and E an exterior algebra over K, both in a finite set of variables. We study rigidity properties of the graded Betti numbers of graded ideals in S and E when passing to their generic initial ideals. First, we prove that if the graded Betti numbers for some i > 1 and k ≥ 0, then for all q ≥ i, where I ⊂ S is a graded ideal. Second, we show that if for some i > 1 and k ≥ 0, then for all q ≥ 1, where I ⊂ E is a graded ideal. In addition, it will be shown that the graded Betti numbers for all i ≥ 1 if and only if I(k) and I(k+1) have a linear resolution. Here I(d) is the ideal generated by all homogeneous elements in I of degree d, and R can be either the polynomial ring or the exterior algebra.

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