Some surfaces with canonical maps of degrees 10, 11, and 14

Fallucca, Federico; Gleissner, Christian A.

doi:10.1002/mana.202200450

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2023

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“…In recent years, this problem attracted the attention of many authors, putting an increased effort in the construction of new examples. As a result, we have now examples in the literature for all degrees 2 ≤ d ≤ 12 and d = 14, 16, 20, 24, 27, 32 and 36, see [11,13,14,[16][17][18][22][23][24][25] and [19].…”

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confidence: 99%

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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