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- W2245286549 abstract "Let $C$ be a Brill-Noether-Petri curve of genus $ggeq 12$. We prove that $C$ lies on a polarised K3 surface (or on a limit of such), if and only if the Wahl map for $C$ is not surjective. The proof is obtained by establishing the validity of two conjectures by J. Wahl. Let $I_C$ be the ideal sheaf of a non-hyperelliptic, genus $g$, canonical curve. The first conjecture states that, if $ggeq 8$, and if the Clifford index of $C$ is greater than 2, then $H^1(bP^{g-1}, I_C^2(k))=0$, for $kgeq 3$. We prove this conjecture for $ggeq 11$. The second conjecture states that a Brill-Noether-Petri curve of genus $ggeq 12$ is extendable, if and only if $C$ lies on a K3 surface. We prove this conjecture admitting, in the statement, limits of polarised K3 surfaces." @default.
- W2245286549 created "2016-06-24" @default.
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- W2245286549 date "2015-07-17" @default.
- W2245286549 modified "2023-09-27" @default.
- W2245286549 title "On two conjectures by J. Wahl" @default.
- W2245286549 hasPublicationYear "2015" @default.
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