BrillNoetherPetri curves on K3 surfaces
Enrico Arbarello (Rome)  Seminar Algebraic Geometry (SAG)
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When 
Jan 14, 2016 from 10:30 am to 11:30 am 
Where  Bonn, Hörsaal MPI, Vivatsgasse 7 
Contact Name  Sachinidis 
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In '86 Lazarsfeld proved that a general hyperplane section of a rank one K3 surface is BrillNoetherPetri (BNP) general, i.e. the map $ H^0( L)\otimes H^0( \omega_CL^{1})\to H^0( \omega_C) $ is injective $\forall$ line bundles $L$ on $C$. In '97, Wahl showed that the nonsurjectivity of the Gaussian map $\nu_1:\wedge ^2H^0( \omega_C)\to H^0( \omega^3_C)$ is a necessary condition for a curve $C$ to be a hyperplane section of a K3 surface (or a limit of such). He conjectured that, for a BNP general curve of genus $g\geq 12$, this condition should also be sufficient. We prove this conjecture (jointly with A. Bruno and E. Sernesi). In a separate work (with A. Bruno, G. Farkas, and G. Saccà) we produce concrete examples of BNP general curves, of any given genus $g$, as degree$3g$ plane curves with eight $g$tuple points and one $(g1)$tuple point and no other singularities (the Du Val curves).