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CANONICALLY FIBERED SURFACES OF GENERAL TYPE

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  18 January 2018

Xin Lü
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Abstract

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In this paper, we construct the first examples of complex surfaces of general type with arbitrarily large geometric genus whose canonical maps induce non-hyperelliptic fibrations of genus $g=4$, and on the other hand, we prove that there is no complex surface of general type whose canonical map induces a hyperelliptic fibrations of genus $g\geqslant 4$ if the geometric genus is large.

Keywords

canonical mapcanonically fibered surfacehyperelliptic fibrationnon-hyperelliptic fibration

MSC classification

Primary: 14J25: Special surfaces 14J29: Surfaces of general type
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 1 , January 2020 , pp. 209 - 229
Copyright
© Cambridge University Press 2018 

Footnotes

This work is supported by SFB/Transregio 45 Periods, Moduli Spaces and Arithmetic of Algebraic Varieties of the Deutsche Forschungsgemeinschaft (DFG), and partially supported by NSFC.

†

Current address: Institut für Mathematik, Universität Mainz, Mainz, Germany, 55099.

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