Koszul cohomology and singular curves
Edoardo Ballico, Claudio Fontanari, Luca Tasin
TL;DR
This paper studies Koszul cohomology on singular curves, proving important conjectures for general k-gonal nodal curves, advancing understanding of algebraic geometry in singular settings.
Contribution
It establishes the validity of Green and Green-Lazarsfeld conjectures for general k-gonal nodal curves, a significant extension of prior results to singular cases.
Findings
Proved Green conjecture for general k-gonal nodal curves.
Proved Green-Lazarsfeld conjecture for the same class.
Extended the understanding of Koszul cohomology on singular curves.
Abstract
We investigate Koszul cohomology on irreducible nodal curves. In particular, we prove both Green and Green-Lazarsfeld conjectures for the general k-gonal nodal curve.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology