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Please use this identifier to cite or link to this item: http://hdl.handle.net/2108/210

Title: Number of moduli of families of plane curves with nodes and cusps
Authors: Ciliberto, Ciro
Galati, Concettina
Issue Date: 23-Feb-2006
Abstract: In my Ph.D.-thesis I computed the number of moduli of certain families of plane curves with nodes and cusps. Let Σn k,d ⊂ P(H0(P2,OP2(n))) := PN, with N = n(n+3)2 , be the closure, in the Zariski’s topology, of the locally closed set of reduced and irreducible plane curves of degree n with k cusps and d nodes. We recall that, if k = 0, the varieties Vn,g = Σn0,d are called the Severi varieties of irreducible plane curves of degree n and geometric genus g = n−1 2  − d. Let Σ⊂ Σn k,d be an irreducible component of Σn k,d and let g = n−1 2 −d−k be the geometric genus of the plane curve corresponding to the general point of Σ. It is naturally defined a rational map ΠΣ : Σ  Mg, sending the general point [Γ] ∈ Σ to the isomorphism class of the normalization of the plane curve Γ corresponding to the point [Γ]. We set number of moduli of Σ := dim(ΠΣ(Σ)). If k < 3n, then (1) dim(ΠΣ(Σ)) ≤ min(dim(Mg), dim(Mg) + ρ − k), where ρ := ρ(2, g, n) = 3n − 2g − 6 is the Brill-Neother n...
URI: http://hdl.handle.net/2108/210
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