A note on normal triple covers over P2 with branch divisors of degree 6

Kodai Mathematical Journal

Taketo Shirane¹ 

[1] Ube National College of Technology

关键词: triple cover;    cubic surface;    torus curve;   

DOI  :  10.2996/kmj/1404393890

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(21)Let S and T be reduced divisors on P2 which have no common components, and Δ = S + 2T. We assume deg Δ = 6. Let π : X → P2 be a normal triple cover with branch divisor Δ, i.e. π is ramified along S (resp. T) with the index 2 (resp. 3). In this note, we show that X is either a P1-bundle over an elliptic curve or a normal cubic surface in P3. Consequently, we give a necessary and sufficient condition for Δ to be the branch divisor of a normal triple cover over P2.

【 授权许可】

Unknown