Calculating the Fundamental Group of Galois Cover of the (2,3)-embedding of ℂℙ1 × T

Amram, Meirav; Tan, Sheng Li; Xu, Wan Yuan; Yoshpe, Michael

doi:10.1007/s10114-020-9220-9

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…in [5] and for embeddings of CP 1 × T of higher degrees by A.-T.-X.-Y. in [9]. In all those works, the Galois covers provide a way to construct important invariants of the base surfaces and contribute to their classification.…”

Section: Introductionmentioning

confidence: 99%

Fundamental group of Galois covers of degree $6$ surfaces

Amram

Gong

Teicher

et al. 2020

Preprint

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In this paper we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of degenerations the fundamental group of the Galois cover is non-trivial and for 20 types it is trivial. Moreover, we compute the Chern numbers of all the surfaces with this type of degeneration and prove that the signatures of all their Galois covers are negative.We formulate a conjecture regarding the structure of the fundamental groups of the Galois covers based on our findings.

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Section: Introductionmentioning

confidence: 99%

Fundamental group of Galois covers of degree $6$ surfaces

Amram

Gong

Teicher

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Non-planar degenerations and related fundamental groups

Amram

2024

European Journal of Mathematics

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Fundamental group of Galois covers of degree 6 surfaces

et al. 2021

View full text Add to dashboard Cite

In this paper, we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of degenerations, the fundamental group of the Galois cover is non-trivial and for 20 types it is trivial. Moreover, we compute the Chern numbers of all the surfaces with this type of degeneration and prove that the signatures of all their Galois covers are negative. We formulate a conjecture regarding the structure of the fundamental groups of the Galois covers based on our findings.

show abstract

Calculating the Fundamental Group of Galois Cover of the (2,3)-embedding of ℂℙ1 × T

Cited by 3 publications

References 17 publications

Fundamental group of Galois covers of degree $6$ surfaces

Fundamental group of Galois covers of degree $6$ surfaces

Non-planar degenerations and related fundamental groups

Fundamental group of Galois covers of degree 6 surfaces

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