On a result of Gelfand, Kapranov, and Zelevinsky
Sean Timothy Paul
TL;DR
This paper provides new elementary proofs for fundamental results by Gelfand, Kapranov, and Zelevinsky, relating discriminants and resultants to determinants of direct images of Cayley-Koszul complexes of sheaves.
Contribution
It introduces simplified, elementary proofs for key algebraic geometry results connecting discriminants, resultants, and Cayley-Koszul complexes.
Findings
Elementary proofs of discriminant and resultant formulas
Expresses these formulas via determinants of Cayley-Koszul complexes
Simplifies understanding of Gelfand, Kapranov, and Zelevinsky's results
Abstract
In this paper I give new elementary proofs of basic results of Gelfand, Kapranov and Zelevinskywhich express discriminants and resultants in terms of determinants of direct images of Cayley-Koszul complexes of sheaves.
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Taxonomy
TopicsMolecular spectroscopy and chirality · Advanced Algebra and Geometry · Axial and Atropisomeric Chirality Synthesis