RMC - Vol. 10, Num. 1

Full paper in PDF:
$%M. Manetti, Automorphisms of generic cycles covers, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 1, 149–156.%$

Automorphisms of Generic Cycles Covers

M. MANETTI

Scuola Normale Superiore
P. Cavaliere 7
I-56126 Pisa — Italy

manetti@sabsns.sns.it

Received: May 29, 1996
Revised: December 9, 1996

ABSTRACT

We generalize an argument of Manetti (1996) for proving a result about automorphisms of generic simple cyclic covers of smooth algebraic varieties. A finite map $p :S-- > X$ is called a simple cyclic cover if there exists an invertible sheaf $L$ on $X$ such that $o+ n -1 p*OS = i=0 L-i$ (cf. Barth et al. (1984), I.17). Here we prove under some “mild” assumptions on the triple $X$ , $L$ , $n$ that for the generic cyclic cover $S$ the group $Aut(S)$ of biregular automorphisms equals the group $mn$ of automorphisms of the branched cover $p$ .

1991 Mathematics Subject Classification: 14E.