Surfaces with pg = q=1, K2=6 and Non-birational Bicanonical Maps

被引：0

作者：

Hu, Yong ^{[1
]}

Zhang, Lei ^{[2
]}

机构：

[1] Korea Inst Adv Study, Sch Math, 85 Hoegiro, Seoul 02455, South Korea

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2019年 / 35卷 / 03期

关键词：

Bicanonical map; algebraic surface; albanese map; GENERAL TYPE;

D O I：

10.1007/s10114-018-7262-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let S be a smooth minimal projective surface of general type with pg(S) = q(S) = 1, K 2S = 6. We prove that the degree of the bicanonical map of S is 1 or 2. So if S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface.

引用

页码：321 / 337

页数：17

共 27 条

[1]

[Anonymous], 1960, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math

[2]

[Anonymous], 2004, A Series of Modern Surveys in Mathematics

[3]

Atiyah M.F., 1957, Proc. Lond. Math. Soc., V7, P414, DOI 10.1112/plms/s3-7.1.414

[4]

Beauville A., 1996, COMPLEX ALGEBRAIC SU

[5]

Beauville Arnaud, 1982, B SOC MATH FRANCE, V110, P343

[6] The classification of surfaces of general type with nonbirational bicanonical map [J].

Borrelli, Giuseppe .

JOURNAL OF ALGEBRAIC GEOMETRY, 2007, 16 (04) :625-669

[7] Surfaces with pg = q=1, K2=8 and nonbirational bicanonical map [J].

Borrelli, Giuseppe .

MANUSCRIPTA MATHEMATICA, 2009, 130 (04) :523-531

[8]

CATANESE F, 1991, S MATH, V32, P49

[9]

Catanese F., 1991, CLASS SURFACES GEN T

[10]

Catanese F., 1999, Contemp. Math., V241, P97

← 1 2 3 →