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On the extendability of projective surfaces and a genus bound for enriques-fano threefolds

Andreas Leopold Knutsen University of Bergen Angelo Felice Lopez Universit`a di Roma Tre Roberto Munoz Universidad Rey Juan Carlos

Differential Geometry mathscidoc:1609.10230

Journal of Differential Geometry, 88, (3), 483-518, 2011
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  17 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.
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@inproceedings{andreas2011on,
  title={ON THE EXTENDABILITY OF PROJECTIVE SURFACES AND A GENUS BOUND FOR ENRIQUES-FANO THREEFOLDS},
  author={Andreas Leopold Knutsen, Angelo Felice Lopez, and Roberto Munoz},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913205005082593891},
  booktitle={Journal of Differential Geometry},
  volume={88},
  number={3},
  pages={483-518},
  year={2011},
}
Andreas Leopold Knutsen, Angelo Felice Lopez, and Roberto Munoz. ON THE EXTENDABILITY OF PROJECTIVE SURFACES AND A GENUS BOUND FOR ENRIQUES-FANO THREEFOLDS. 2011. Vol. 88. In Journal of Differential Geometry. pp.483-518. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913205005082593891.
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