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

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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

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