A twisted bicanonical system with base points

Autor: Roberto Pignatelli, Filippo F. Favale
Přispěvatelé: Favale, F, Pignatelli, R
Rok vydání: 2017
Předmět:
Zdroj: ANNALI DELL'UNIVERSITA' DI FERRARA. 63:113-131
ISSN: 1827-1510
0430-3202
DOI: 10.1007/s11565-017-0273-3
Popis: By a theorem of Reider, a twisted bicanonical system, that means a linear system of divisors numerically equivalent to a bicanonical divisor, on a minimal surface of general type, is base point free if $K^2_S \geq 5$. Twisted bicanonical systems with base points are known in literature only for $K^2=1,2$. We prove in this paper that all surfaces in a family of surfaces with $K^2=3$ constructed in a previous paper with G. Bini and J. Neves have a twisted bicanonical system (different from the bicanonical system) with two base points. We show that the map induced by the above twisted bicanonical system is birational, and describe in detail the closure of its image and its singular locus. Inspired by this description, we reduced the problem of constructing a minimal surface of general type with $K^2=3$ whose bicanonical system has base points, under some reasonable assumptions, to the problem of constructing a curve in $\mathbb{P}^3$ with certain properties.
Comment: 20 pages. Corrected an error in Theorem 3. Some arguments have been simplified. To appear on Annali dell'Universit\`a di Ferrara, in a special volume dedicated to the memory of Alexandru Lascu
Databáze: OpenAIRE
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