A genus explanation of the Buchsbaum-Rim multiplicity
Vinicius Bou\c{c}a, Thiago Fiel, Seyed Hamid Hassanzadeh, Jos\'e, Na\'eliton
TL;DR
This paper provides a new geometric interpretation of the Buchsbaum-Rim multiplicity as the arithmetic genus of Koszul homology sheaves, using spectral sequences to connect algebraic and geometric perspectives.
Contribution
It introduces a novel approach to understanding the Buchsbaum-Rim multiplicity via Koszul-cech spectral sequences and relates it to the arithmetic genus of associated sheaves.
Findings
Buchsbaum-Rim multiplicity equals the Euler characteristic of Koszul homology sheaves.
Establishes a geometric interpretation of algebraic multiplicity.
Connects spectral sequences with geometric invariants.
Abstract
We study the Buchsbaum-Rim multiplicity, ab inicio, through a Koszul-\v{C}ech spectral sequence. We show that the Buchsbaum-Rim multiplicity is the arithmetic genus (Euler characteristic) of Koszul homology sheaves on a projective space over the base scheme.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics