Wahl maps and extensions of canonical curves and K3 surfaces
Résumé
Let C be a smooth projective curve (resp. (S,L) a polarized K3 surface) of genus g⩾11, with Clifford index at least 3, considered in its canonical embedding in Pg−1 (resp. in its embedding in |L|∨≅Pg). We prove that C (resp. S) is a linear section of an arithmetically Gorenstein normal variety Y in Pg+r, not a cone, with dim(Y)=r+2 and ωY=OY(−r), if the cokernel of the Gauss–Wahl map of C (resp. H1(TS⊗L∨)) has dimension larger than or equal to r+1 (resp. r). This relies on previous work of Wahl and Arbarello–Bruno–Sernesi. We provide various applications.
Domaines
Géométrie algébrique [math.AG]
Origine : Fichiers produits par l'(les) auteur(s)
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