Higher Gaussian Maps on K3 Surfaces

Higher Gaussian Maps on K3 Surfaces

We give sufficient conditions for the surjectivity of higher Gaussian maps on a polarized K3 surface. As an application, we show that the $k$-th Gaussian map for a general curve of genus $g$ (that depends quadratically with $k$) is surjective. Along the proof, we also exhibit an ampleness criterion...

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Veröffentlicht in:International mathematics research notices 2024-05, Vol.2024 (10), p.8185-8212
1. Verfasser: Ríos Ortiz, Ángel David
Format: Artikel
Sprache:eng
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Zusammenfassung:We give sufficient conditions for the surjectivity of higher Gaussian maps on a polarized K3 surface. As an application, we show that the $k$-th Gaussian map for a general curve of genus $g$ (that depends quadratically with $k$) is surjective. Along the proof, we also exhibit an ampleness criterion for divisors in the Hilbert scheme of two points of a K3 surface.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnad165