We introduce a technique based on Gaussian maps to study whether a surface can lie on a threefold as a very ample divisor with given normal bundle. We give applications, among which one to surfaces of general type and another to Enriques surfaces. In particular, we prove the genus bound g < 18 for Enriques-Fano threefolds. Moreover we find a new Enriques-Fano threefold of genus 9 whose normalization has canonical but not terminal singularities and does not admit Q-smoothings.
Knutsen, A.L., Lopez, A., Munoz, R. (2011). On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds. JOURNAL OF DIFFERENTIAL GEOMETRY, 88, 483-518.
On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds
LOPEZ, Angelo;
2011-01-01
Abstract
We introduce a technique based on Gaussian maps to study whether a surface can lie on a threefold as a very ample divisor with given normal bundle. We give applications, among which one to surfaces of general type and another to Enriques surfaces. In particular, we prove the genus bound g < 18 for Enriques-Fano threefolds. Moreover we find a new Enriques-Fano threefold of genus 9 whose normalization has canonical but not terminal singularities and does not admit Q-smoothings.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
