scholarly journals Free resolutions for polynomial functors

2004 ◽  
Vol 271 (1) ◽  
pp. 22-64 ◽  
Author(s):  
Alexandre Tchernev ◽  
Jerzy Weyman
Keyword(s):  
Free Resolutions ◽  
Polynomial Functors

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

scholarly journals The monoidal structure on strict polynomial functors

2017 ◽  
Vol 485 ◽  
pp. 213-229 ◽  
Author(s):  
Cosima Aquilino ◽  
Rebecca Reischuk
Keyword(s):  
Monoidal Structure ◽  
Polynomial Functors

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

Free Resolutions

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

scholarly journals The temporal logic of coalgebras via Galois algebras

2002 ◽  
Vol 12 (6) ◽  
pp. 875-903 ◽  
Author(s):  
BART JACOBS
Keyword(s):  
State Space ◽  
Temporal Logic ◽  
Metric Spaces ◽  
Linear Temporal Logic ◽  
The State ◽  
Temporal Logics ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Polynomial Functors

This paper introduces a temporal logic for coalgebras. Nexttime and lasttime operators are defined for a coalgebra, acting on predicates on the state space. They give rise to what is called a Galois algebra. Galois algebras form models of temporal logics like Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). The mapping from coalgebras to Galois algebras turns out to be functorial, yielding indexed categorical structures. This construction gives many examples, for coalgebras of polynomial functors on sets. More generally, it will be shown how ‘fuzzy’ predicates on metric spaces, and predicates on presheaves, yield indexed Galois algebras, in basically the same coalgebraic manner.

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.

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