RT Journal Article
T1 On the existence of Enriques-Fano threefolds of index greater than one
A1 Giraldo Suárez, Luis
A1 Lopez, Angelo Felice
A1 Muñoz, Roberto
AB Let X C P-N be an irreducible threefold having a hyperplane section Y that is a smooth Enriques surface and such that X is not a cone over Y. In 1938 Fano claimed a classification of such threefolds; however, due to gaps in his proof, the problem still remains open. In this article we solve the case when Y is the r-th Veronese embedding, for r greater than or equal to 2, of another Enriques surface, by proving that there are no such X. The latter is achieved, among other things, by a careful study of trisecant lines to Enriques surfaces. As another consequence we get precise information on the ideal of an Enriques surface. In a previous paper we had proved that any smooth linearly normal Enriques surface has homogeneous ideal generated by quadrics and cubics. Here we are able to specify when the quadrics are enough, at least scheme-theoretically.
PB American Mathematical Society
SN 1056-3911
YR 2004
FD 2004
LK https://hdl.handle.net/20.500.14352/50108
UL https://hdl.handle.net/20.500.14352/50108
LA eng
NO DGES
NO MURST national project "Geometria Algebrica"
DS Docta Complutense
RD 1 jul 2025