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July 2011 On the Extendability of Projective Surfaces and a Genus Bound for Enriques-Fano Threefolds
Andreas Leopold Knutsen, Angelo Felice Lopez, Roberto Muñoz
J. Differential Geom. 88(3): 483-518 (July 2011). DOI: 10.4310/jdg/1321366357

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 $g \le17$ 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 $\mathbb{Q}$-smoothings.

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Andreas Leopold Knutsen. Angelo Felice Lopez. Roberto Muñoz. "On the Extendability of Projective Surfaces and a Genus Bound for Enriques-Fano Threefolds." J. Differential Geom. 88 (3) 483 - 518, July 2011. https://doi.org/10.4310/jdg/1321366357

Information

Published: July 2011
First available in Project Euclid: 15 November 2011

zbMATH: 1238.14026
MathSciNet: MR2844440
Digital Object Identifier: 10.4310/jdg/1321366357

Rights: Copyright © 2011 Lehigh University

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Vol.88 • No. 3 • July 2011
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