Canonical maps of surfaces defined by abelian covers

Du, Rong; Gao, Yun

doi:10.4310/ajm.2014.v18.n2.a2

Cited by 13 publications

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References 1 publication

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“…From Proposition 1.1, it is an interesting problem to know the geometric realization of possible canonical degrees and many surfaces with canonical degree at most 16 have been constructed, see [9,15] for more references. However, the first example of a surface with maximal canonical degree 36 was constructed only recently by [19] as a suitably chosen C 2 × C 2 -Galois cover of a special fake projective plane X.…”

Section: Introductionmentioning

confidence: 99%

Examples of Surfaces with Canonical Map of Maximal Degree

Lai

Yeung

2021

Taiwanese J. Math.

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It was shown by Beauville that if the canonical map ϕ |K M | of a complex smooth projective surface M is generically finite, then deg(ϕ |K M | ) ≤ 36. The first example of a surface with canonical degree 36 was found by the second author. In this article, we show that for any surface which is a degree four Galoisétale cover of a fake projective plane X with the largest possible automorphism group Aut(X) = C 7 : C 3 (the unique non-abelian group of order 21), the base locus of the canonical map is finite, and we verify that 35 of these surfaces have maximal canonical degree 36. We also classify all smooth degree four Galoisétale covers of fake projective planes, which give possible candidates for surfaces of canonical degree 36. Finally, we also confirm in this paper the optimal upper bound of the canonical degree of smooth threefolds of general type with sufficiently large geometric genus, related to earlier work of Hacon and Cai.

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Section: Introductionmentioning

confidence: 99%

Examples of Surfaces with Canonical Map of Maximal Degree

Lai

Yeung

2021

Taiwanese J. Math.

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“…It is worth mentioning that the canonical map of the surface constructed by U. Persson is an abelian cover of P 2 . In [5], R. Du and Y. Gao showed that if the canonical map is an abelian cover of P 2 of degree d > 8, then d = 9 or 16.…”

Section: Introductionmentioning

confidence: 99%

A new example of an algebraic surface with canonical map of degree 16

Bin

2019

Arch. Math.

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“…The approach to construct these surfaces is using Z 3 2 −covers with some appropriate branch loci. Note that canonical maps defined by abelian covers of P 2 , and in particular the abelian covers with the group Z 3 2 , have been studied very explicitly by Rong Du and Yun Gao in [5].…”

Section: Introductionmentioning

confidence: 99%