ProV Logo
0
Examples of surfaces with canonical maps...
Lai, Ching-Jui...

Free

Examples of surfaces with canonical maps of maximal degree by Lai, Ching-Jui ( Author )
Lemonjar Open Access
N.A
24-10-2015
It was shown by A. Beauville that if the canonical map φ|KM| of a complex smooth projective surface M is generically finite, then deg(φ|KM|)≤36. The first example of a surface with canonical degree 36 was found by the second author. In this article, we show that for any surface which is a degree four Galois étale cover of a fake projective plane X with the largest possible automorphism group Aut(X)=C7:C3 (the unique non-abelian group of order 21), the base locus of the canonical map is finite, and we verify that 35 of these surfaces have maximal canonical degree 36. We also classify all smooth degree four Galois étale covers of fake projective planes, which give possible candidates for surfaces of canonical degree 36. Finally, we also confirm in this paper the optimal upper bound of the canonical degree of smooth threefolds of general type with sufficiently large geometric genus, related to earlier work of C. Hacon and J.-X. Cai.
-
Article
pdf
36.88 KB
English
-
MYR 0.00
-
http://arxiv.org/abs/1510.07097
Share this eBook