Quasi-complete intersections in P2 and syzygies
Abstract
Let C ∈ P2 be a reduced, singular curve of degree d and equation f = 0. Let denote the jacobian subscheme of C. We have 0 -> E -> 3.O -> I(d-1) -> 0 (the surjection is given by the partials of f). We study the relationships between the Betti numbers of the module H0*(E) and the integers, d; τ, where τ = deg(). We observe that our results apply to any quasi-complete intersection of type (s; s; s).
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