Quasi-complete intersections in P2 and syzygies

Abstract

Let C \in P2 be a reduced, singular curve of degree d and equation f = 0. Let Σdenote the jacobian subscheme of C. We have 0 -> E -> 3.O -> I_Σ(d-1) -> 0 (the surjection is given by the partials of f). We study the relationships between the Betti numbers of the module H^0_*(E) and the integers, d; τ, where τ= deg(Σ). We observe that our results apply to any quasi-complete intersection of type (s; s; s).

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References in corpus (2)

• Jacobian syzygies and plane curves with maximal global Tjurina numbers
• On the cohomology of rank two vector bundles on P2 and a theorem of Chiantini and Valabrega

Cited by in corpus (1)

• Jacobian syzygies and plane curves with maximal global Tjurina numbers