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 : firstname.lastname@example.org Lei ZHANG School of Mathematical Science, University of Science and Technology of China, Hefei 230026,P. R.China E-mail : email@example.com 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
Acta Mathematica Sinica, English Series – Springer Journals
Published: May 18, 2018
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
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
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.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera