Diagonal Double Kodaira Structures on Finite Groups

Polizzi, Francesco

doi:10.1007/978-3-030-87502-2_12

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2022

2024

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Cited by 4 publications

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“…The original examples by Atiyah, Hirzebruch and Kodaira have slope lying in (2, 2 + 1/3], (see [6, p. 221]), and the first examples with higher slope were given by Catanese and Rollenske in [9] using double Kodaira that satisfy ν(S) = 2 + 2/3. More examples of double Kodaira fibrations where given by Causin and Polizzi in [10] and further explored by Polizzi in [34]. At present it is unknown whether the slope of a Kodaira fibred surface can be arbitrarily close to 3.…”

Section: 2mentioning

confidence: 99%

25 open questions about vector bundles and their moduli

Ballico

Gasparim

Rubilar

2022

Proyecciones (Antofagasta)

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Section: 2mentioning

confidence: 99%

25 open questions about vector bundles and their moduli

Ballico

Gasparim

Rubilar

2022

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Finite Quotients of Surface Braid Groups and Double Kodaira Fibrations

Polizzi

Sabatino²

2023

Trends in Mathematics

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Extra-special quotients of surface braid groups and double Kodaira fibrations with small signature

Polizzi

Sabatino²

2022

Geom Dedicata

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We study some special systems of generators on finite groups, introduced in previous work by the first author and called diagonal double Kodaira structures, in order to investigate finite non-abelian quotients of the pure braid group on two strands $${\mathsf {P}}_2(\Sigma _b)$$ P 2 ( Σ b ) , where $$\Sigma _b$$ Σ b is a closed Riemann surface of genus b. In particular, we prove that, if a finite group G admits a diagonal double Kodaira structure, then $$|G|\ge 32$$ | G | ≥ 32 , and equality holds if and only if G is extra-special. In the last section, as a geometrical application of our algebraic results, we construct two 3-dimensional families of double Kodaira fibrations having signature 16. Such surfaces are different from the ones recently constructed by Lee, Lönne and Rollenske and, as far as we know, they provide the first examples of positive-dimensional families of double Kodaira fibrations with small signature.

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Diagonal Double Kodaira Structures on Finite Groups

Cited by 4 publications

References 9 publications

25 open questions about vector bundles and their moduli

25 open questions about vector bundles and their moduli

Finite Quotients of Surface Braid Groups and Double Kodaira Fibrations

Extra-special quotients of surface braid groups and double Kodaira fibrations with small signature

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