Abstract
We consider the quotient X of bi-elliptic surface by a finite automorphism group. If X is smooth, then it is a bi-elliptic surface or ruled surface with irregularity one. As a corollary any bi-elliptic surface cannot be Galois covering of projective plane, hence does not have any Galois embedding.
Highlights
1 Statement of result We consider a covering of surface, i.e., let X1 and X2 be connected normal complex surfaces and π : X1 −→ X2 a finite surjective proper holomorphic map
2007) In this note we consider the case where X1 is a bi-elliptic surface and π is a Galois covering
Definition 1 A bi-elliptic surface is a surface with the geometric genus zero and having an abelian surface as its unramified covering
Summary
1 Statement of result We consider a covering of surface, i.e., let X1 and X2 be connected normal complex surfaces and π : X1 −→ X2 a finite surjective proper holomorphic map. 2007) In this note we consider the case where X1 is a bi-elliptic surface and π is a Galois covering. First we note the following: Remark 2 Let S be a bi-elliptic surface. If π : S −→ X is a Galois covering and X is smooth, X has no curve with negative self-intersection number.
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