Free Resolutions

1998 ◽  
pp. 234-289 ◽  
Author(s):  
David Cox ◽  
John Little ◽  
Donal O’Shea
Keyword(s):  
Free Resolutions

scholarly journals Free resolutions of some Schubert singularities in the Lagrangian Grassmannian

2015 ◽  
Vol 279 (1-2) ◽  
pp. 329-355
Author(s):  
Venkatramani Lakshmibai ◽  
Reuven Hodges
Keyword(s):  
Free Resolutions ◽  
Lagrangian Grassmannian

Free resolutions for deformations of maximal cohen-macaulay modules

2000 ◽  
Vol 28 (11) ◽  
pp. 5329-5352 ◽  
Author(s):  
Liam O'Carroll ◽  
Dorin Popescu
Keyword(s):  
Free Resolutions

On the Computation of Minimal Free Resolutions with Integer Coefficients

2019 ◽  
pp. 51-72
Author(s):  
Soda Diop ◽  
Guy Mobouale Wamba ◽  
Andre Saint Eudes Mialebama Bouesso ◽  
Djiby Sow
Keyword(s):  
Free Resolutions ◽  
Integer Coefficients ◽  
Minimal Free Resolutions

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.

scholarly journals Generic free resolutions and root systems

2018 ◽  
Vol 68 (3) ◽  
pp. 1241-1296
Author(s):  
Jerzy Weyman
Keyword(s):  
Root Systems ◽  
Free Resolutions

scholarly journals Stably free resolutions of lattices over finite groups

1990 ◽  
Vol 49 (3) ◽  
pp. 364-385
Author(s):  
K. W. Gruenberg
Keyword(s):  
Euler Characteristic ◽  
Finite Groups ◽  
Class Group ◽  
Free Resolution ◽  
Free Resolutions ◽  
Minimal Free Resolution ◽  
Residue Classes ◽  
Projective Class

AbstractFor a ZG-lattice A, the nth partial free Euler characteristic εn(A) is defined as the infimum of all where F* varies over all free resolutions of A. It is shown that there exists a stably free resolution E* of A which realises εn(A) for all n≥0 and that the function n → εn(A) is ultimately polynomial no residue classes. The existence of E* is established with the help of new invariants σn(A) of A. These are elements in certain image groups of the projective class group of ZG. When ZG allows cancellation, E* is a minimal free resolution and is essentially unique. When A is periodic, E* is ultimately periodic of period a multiple of the projective period of A.

scholarly journals Determinantal ideals without minimal free resolutions

1990 ◽  
Vol 118 ◽  
pp. 203-216 ◽  
Author(s):  
Mitsuyasu Hashimoto
Keyword(s):  
Free Resolution ◽  
Unit Element ◽  
Free Resolutions ◽  
Minimal Free Resolution ◽  
Determinantal Ideals ◽  
Arbitrary Base ◽  
Generic Matrix ◽  
Base Ring ◽  
Minimal Free Resolutions ◽  
The Ideal

Let R be a Noetherian commutative ring with, unit element, and Xij be variables with 1 ≤ i ≤ m and 1 ≤ j ≤ n. Let S = R[xij] be the polynomial ring over R, and It be the ideal in S, generated by the t × t minors of the generic matrix (xij) ∈ Mm, n(S). For many years there has been considerable interest in finding a minimal free resolution of S/It, over arbitrary base ring R. If we have a minimal free resolution P. over R = Z, the ring of integers, then R′ ⊗z P. is a resolution of S/It over the base ring R′.

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