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Pruned cellular free resolutions of monomial ideals

Author
Alvarez, J.; Fernández Ramos, O.; Gimenez, P.
Type of activity
Journal article
Journal
Journal of algebra
Date of publication
2020-01-01
Volume
541
First page
126
Last page
145
DOI
10.1016/j.jalgebra.2019.09.013
Repository
http://hdl.handle.net/2117/175476 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S0021869319305009 Open in new window
Abstract
Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal. The pruned resolution is not simplicial in general, but we can slightly modify our algorithm in order to obtain a simplicial resolution. We also show that the Lyubeznik resolution fits into our pruning strategy. The pruned resolution is not always minimal but it is a lot closer to the minimal resolution tha...
Citation
Alvarez, J.; Fernández Ramos, O.; Gimenez, P. Pruned cellular free resolutions of monomial ideals. "Journal of algebra", 1 Gener 2020, vol. 541, p. 126-145.
Keywords
Betti splitting, Discrete Morse theory, Free resolution, Monomial ideal
Group of research
GEOMVAP - Geometry of Manifolds and Applications

Participants