HYPERELLIPTIC SURFACES WITH K2 < 4χ-6

被引：0

作者：

Rito, Carlos ^{[1
]}

Marti Sanchez, Maria ^{[2
]}

机构：

[1] Univ Tras Os Montes & Alto Douro, Dept Matemat, P-5001801 Vila Real, Portugal

[2] Nebrija Univ, Madrid 28040, Spain

来源：

OSAKA JOURNAL OF MATHEMATICS | 2015年 / 52卷 / 04期

关键词：

GENERAL TYPE; ALGEBRAIC-SURFACES; BICANONICAL MAP;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S be a smooth minimal surface of general type with a (rational) pencil of hyperelliptic curves of minimal genus g. We prove that if K-S(2) < 4 chi (O-S)-6, then g is bounded. The surface S is determined by the branch locus of the covering S -> S/i, where i is the hyperelliptic involution of S. For K-S(2) < 3 chi (O-S)-6, we show how to determine the possibilities for this branch curve. As an application, given g > 4 and K-S(2) - 3 chi (O-S) < -6, we compute the maximum value for chi(O-S). This list of possibilities is sharp.

引用

页码：929 / 945

页数：17

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