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SUBCOMPLEXES OF CERTAIN FREE RESOLUTIONS

Part of: Commutative algebra: Homological methods

Published online by Cambridge University Press:  25 March 2024

MAYA BANKS Open the ORCID record for MAYA BANKS [Opens in a new window]  and
ALEKSANDRA SOBIESKA Open the ORCID record for ALEKSANDRA SOBIESKA [Opens in a new window]
MAYA BANKS
Affiliation:
Department of Mathematics University of Wisconsin–Madison 480 Lincoln Drive 53706 Madison, WI United States [email protected]
ALEKSANDRA SOBIESKA*
Affiliation:
Department of Mathematics University of Wisconsin–Madison 480 Lincoln Drive 53706 Madison, WI United States
*
[email protected]
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Abstract

We invoke the Bernstein–Gel$'$fand–Gel$'$fand (BGG) correspondence to study subcomplexes of free resolutions given by two well-known complexes, the Koszul and the Eagon–Northcott. This approach provides a complete characterization of the ranks of free modules in a subcomplex in the Koszul case and imposes numerical restrictions in the Eagon–Northcott case.

Keywords

subcomplexfree resolutionBGG correspondenceKoszul complexEagon–Northcott

MSC classification

Primary: 13D02: Syzygies, resolutions, complexes 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
Type
Article
Information
Nagoya Mathematical Journal , Volume 256 , December 2024 , pp. 886 - 904
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

The first author was partially supported by the National Science Foundation (Grant No. DMS-1902123).

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