Involutions on numerical Campedelli surfaces

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概要

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• Numerical Campedelli surfaces are minimal surfaces of general type with vanishing geometric genus and canonical divisor with self-intersection 2. Although they have been studied by several authors,their complete classification is not known. In this paper we classify numerical Campedelli surfaces with an involution, i.e., an automorphism of order 2. First we show that an involution on a numerical Campedelli surface $S$ has either four or six isolated fixed points, and the bicanonical map of $S$ is composed with the involution if and only if the involution has six isolated fixed points. Then we study in detail each of the possible cases, describing also several examples.

• 東北大学の論文

著者

• Mendes Lopes

  Departamento De Matematica Instituto Superior Tecnico Universidade Tecnica De Lisboa

• Pardini Rita

  Dipartimento di Matematica, Universita di Pisa

• Calabri Alberto

  Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universita degli Studi di Pado

• Pardini Rita

  Dipartimento Di Matematica Universita Degli Studi Di Pisa

関連論文

• THE ORDER OF FINITE ALGEBRAIC FUNDAMENTAL GROUPS OF SURFACES WITH $K^2 \le 3χ-2$(Algebraic Geometry and Topology)
• Irregular canonical double surfaces
• Involutions on numerical Campedelli surfaces

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