Mathematics – Algebraic Geometry
Scientific paper
2006-05-30
Mathematics
Algebraic Geometry
Slight change in the statements (and proofs) of Prop.1.4 and of Prop.16.1. Added Rmk. 16.2. We thank J\'anos Koll\'ar for poin
Scientific paper
We introduce a new technique, based on Gaussian maps, to study the possibility, for a given surface, to lie on a threefold as a very ample divisor with given normal bundle. We give several applications, among which one to surfaces of general type and another one to Enriques surfaces. For the latter we prove that any threefold (with no assumption on its singularities) having as hyperplane section a smooth Enriques surface (by definition an Enriques-Fano threefold) has genus g < 18 (where g is the genus of its smooth curve sections). The latter bound was also proved recently by Prokhorov, who also found an example of genus 17. 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 Andreas Leopold
Lopez Angelo Felice
Muñoz Roberto
No associations
LandOfFree
On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-467399