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 : email@example.com Lei ZHANG School of Mathematical Science, University of Science and Technology of China, Hefei 230026,P. R.China E-mail : firstname.lastname@example.org 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
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