# Surfaces with p g = q = 1, K 2 = 6 and Non-birational Bicanonical Maps

Surfaces with p g = q = 1, K 2 = 6 and Non-birational Bicanonical Maps Let S be a smooth minimal projective surface of general type with p g (S) = q(S) = 1, K S 2 = 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

# Surfaces with p g = q = 1, K 2 = 6 and Non-birational Bicanonical Maps

, Volume 35 (3) – May 18, 2018
17 pages

/lp/springer_journal/surfaces-with-p-g-q-1-k-2-6-and-non-birational-bicanonical-maps-jBcu5UCQWz

# References (40)

Publisher
Springer Journals
Copyright © 2018 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
DOI
10.1007/s10114-018-7262-z
Publisher site
See Article on Publisher Site

### Abstract

Let S be a smooth minimal projective surface of general type with p g (S) = q(S) = 1, K S 2 = 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.

### Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 18, 2018