Topological types of actions on curves

Conti, Diego; Ghigi, Alessandro; Pignatelli, Roberto

doi:10.1016/j.jsc.2023.01.002

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“…The first example has been found by using the database [10]. Later on, we have run a systematic search over all automorphisms of S 3 ×Z 2 3 , proving that the obtained surfaces having only nodes are isomorphic to the four surfaces presented in this note.…”

Section: Remark 21mentioning

confidence: 80%

Examples of surfaces with canonical maps of degree 12, 13, 15, 16 and 18

Fallucca

2023

Annali di Matematica

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In this note, we present examples of complex algebraic surfaces with canonical maps of degree 12, 13, 15, 16 and 18. They are constructed as quotients of a product of two curves of genus 10 and 19 using certain non-free actions of the group $$S_3\times {\mathbb {Z}}_3^2$$ S 3 × Z 3 2 . To our knowledge, there are no other examples in the literature of surfaces with canonical map of degree 13, 15 and 18.

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Section: Remark 21mentioning

confidence: 80%