Fundamental group of Galois covers of degree 6 surfaces

M. Amram, C. Gong, U. Sinichkin, S. L. Tan, W. Y. Xu, M. Yoshpe

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)593-613
Number of pages21
JournalJournal of Topology and Analysis
Volume15
Issue number3
DOIs
StatePublished - 1 Sep 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 World Scientific Publishing Company.

Keywords

  • Degeneration
  • Galois cover
  • braid monodromy
  • fundamental group
  • generic projection

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