# 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 Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 18, 2018 https://doi.org/10.1007/s10114-018-7262-z English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 Surfaces with p = q =1, K = 6 and Non-birational Bicanonical Maps Yong HU School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455,South Korea E-mail : yonghu11@kias.re.kr Lei ZHANG School of Mathematical Science, University of Science and Technology of China, Hefei 230026,P. R.China E-mail : zhlei18@ustc.edu.cn Abstract Let S be a smooth minimal projective surface of general type with p (S)= q(S)=1, K = 6. We prove that the degree of the bicanonical map of S is 1or2. Soif S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface. Keywords Bicanonical map, algebraic surface, albanese map MR(2010) Subject Classiﬁcation 14J29 1 Introduction Surfaces of general type with small invariants p and χ are of special interest in the classiﬁcation theory. For a smooth minimal projective surface of general type S with p (S)= q(S) = 1, it is known that 2 ≤ K ≤ 9, and (1) if K =2, 3, it is characterized by means of 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 OnlineFirst – May 18, 2018
17 pages
Loading next page...

/lp/springer_journal/surfaces-with-p-g-q-1-k-2-6-and-non-birational-bicanonical-maps-jBcu5UCQWz
Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Copyright
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
D.O.I.
10.1007/s10114-018-7262-z
Publisher site
See Article on Publisher Site

### Abstract

Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 18, 2018 https://doi.org/10.1007/s10114-018-7262-z English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 Surfaces with p = q =1, K = 6 and Non-birational Bicanonical Maps Yong HU School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455,South Korea E-mail : yonghu11@kias.re.kr Lei ZHANG School of Mathematical Science, University of Science and Technology of China, Hefei 230026,P. R.China E-mail : zhlei18@ustc.edu.cn Abstract Let S be a smooth minimal projective surface of general type with p (S)= q(S)=1, K = 6. We prove that the degree of the bicanonical map of S is 1or2. Soif S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface. Keywords Bicanonical map, algebraic surface, albanese map MR(2010) Subject Classiﬁcation 14J29 1 Introduction Surfaces of general type with small invariants p and χ are of special interest in the classiﬁcation theory. For a smooth minimal projective surface of general type S with p (S)= q(S) = 1, it is known that 2 ≤ K ≤ 9, and (1) if K =2, 3, it is characterized by means of

### Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 18, 2018

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off