A surface with canonical map of degree 24

Rito, Carlos

doi:10.1142/s0129167x17500410

Cited by 17 publications

(12 citation statements)

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“…The explicit computation is accomplished by using Magma. The proof of Theorem 1.4 generalizes the argument of [19], see also the Corrigendum in [19] and [17].…”

Section: Introductionmentioning

confidence: 63%

“…It is proved that 2 i=0 Z t 2 i = ∅, which was verified in the Corrigendum of [19] by checking that 2 i=0 Z t 2 i = ∅ on X modulo p = 23 from the command HilbertPolynomial in Magma. We remark that the same example was also studied later in [17], where the author independently verified with more sophisticated techniques in Magma that the sections obtained from the above procedure do give rise to sections in H 0 (M, K M ). Now under the action of G 7 , the explicit sections t 0 and a j t i , i = 1, 2 and 0 ≤ j ≤ 6, precisely give the effective sections of S := Σ∈C 4 2 −{1} H 0 (X, K + Σ).…”

Section: New Examples Of Surfaces With Maximal Canonical Degreementioning

confidence: 68%

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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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“…The explicit computation is accomplished by using Magma. The proof of Theorem 1.4 generalizes the argument of [19], see also the Corrigendum in [19] and [17].…”

Section: Introductionmentioning

confidence: 63%

Section: New Examples Of Surfaces With Maximal Canonical Degreementioning

confidence: 68%

Examples of Surfaces with Canonical Map of Maximal Degree

Lai

Yeung

2021

Taiwanese J. Math.

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“…Later, G. Xiao improved this result by showing that if the geometric genus of X is bigger than 132, the degree of the canonical map is less than or equal to 8 (see [14,Theorem 3]). Only few surfaces with d greater than 8 have been known so far, such as: S. L. Tan's example [13] with d = 9, U. Persson's example [9] with d = 16 and C. Rito's examples [10], [12], [11] with d = 12, 16, 24. There is a recent preprint [6] of C. Gleissner, R. Pignatelli and C. Rito constructing surfaces with d = 24, q = 1 and d = 32, q = 0, where q = dim H 1 (X, K X ) is the irregularity of X.…”

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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“…Another open question in this direction is to determine the positive degree of the canonical map. Progress in this direction for surfaces appears in [Bea], [Tan], [Cas], [Per], [D-G1], [Rit1], [Rit2], [Rit3], [Yeung] and for 3-folds in [D-G2], [Cai]. Explicit examples are often constructed by taking abelian covers.…”

Section: Introductionmentioning

confidence: 99%

On Abelian Canonical $n$-folds of General Type

Du¹,

Gao²

2017

Taiwanese J. Math.

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Let X be a Gorenstein minimal projective n-fold with at worst locally factorial terminal singularities, and suppose that the canonical map of X is generically finite onto its image. When n < 4, the canonical degree is universally bounded. While the possibility of obtaining a universal bound on the canonical degree of X for n 4 may be inaccessible, we give a uniform upper bound for the degrees of certain abelian covers. In particular, we show that if the canonical divisor K X defines an abelian cover over P n , i.e., when X is an abelian canonical n-fold, then the canonical degree of X is universally upper bounded by a constant which only depends on n for X non-singular. We also construct two examples of non-singular minimal projective 4-folds of general type with canonical degrees 81 and 128.

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A surface with canonical map of degree 24

Abstract: We construct a complex algebraic surface with geometric genus pg = 3, irregularity q = 0, self-intersection of the canonical divisor K 2 = 24 and canonical map of degree 24 onto P 2 . 2010 MSC: 14J29.

Cited by 17 publications

References 15 publications

Examples of Surfaces with Canonical Map of Maximal Degree

Examples of Surfaces with Canonical Map of Maximal Degree

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

On Abelian Canonical $n$-folds of General Type

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