Let $L$ be a very ample line bundle on a smooth complex projective variety $X$ of dimension $\geq 7$ . We classify the polarized manifolds $(X, L)$ such that there exists a smooth member $A$ of $| L |$ endowed with a branched covering of degree five $\pi : A \rightarrow \bm{P}^{n}$ . The cases of $\deg \pi =2$ and $3$ are already studied by Lanteri-Palleschi-Sommese.
Publié le : 2006-10-14
Classification:
polarized variety,
hyperplane section,
branched covering,
linear system,
graded ring,
14C20,
14J40,
14H30,
14H45,
14N30
@article{1179759539,
author = {AMITANI, Yasuharu},
title = {Projective manifolds with hyperplane sections being five-sheeted covers of projective space},
journal = {J. Math. Soc. Japan},
volume = {58},
number = {3},
year = {2006},
pages = { 1119-1131},
language = {en},
url = {http://dml.mathdoc.fr/item/1179759539}
}
AMITANI, Yasuharu. Projective manifolds with hyperplane sections being five-sheeted covers of projective space. J. Math. Soc. Japan, Tome 58 (2006) no. 3, pp. 1119-1131. http://gdmltest.u-ga.fr/item/1179759539/