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

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

doi:10.1007/s10114-020-9220-9

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

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

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

As known to all, it is quite difficult to compute the fundamental group of a surface of general type. In this paper, applying Moishezon-Teicher’s algorithm, we investigate the fundamental group of a special surface of general type with zero topological index, namely, the Galois cover of the (2,3)-embedding of ℂℙ¹ × T. Because the full presentation of the group is very complicated, we compute its special quotient and get an interesting result about its structure.

Original language	English
Pages (from-to)	273-291
Number of pages	19
Journal	Acta Mathematica Sinica, English Series
Volume	36
Issue number	3
DOIs	https://doi.org/10.1007/s10114-020-9220-9
State	Published - 1 Mar 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany & The Editorial Office of AMS.

Funding

Supported by the ISF-NSFC joint research program (Grant No. 2452/17), NSF of China, MST of China (Grant No. 2018AAA0101001) and STC of Shanghai (Grant No. 18dz2271000) Acknowledgements

Funders	Funder number
ISF-NSFC	2452/17
STC of Shanghai	18dz2271000
National Science Foundation
Ministry of Science and Technology of the People's Republic of China	2018AAA0101001

Keywords

14N20
14Q10
20F36
32S22
52C35
Fundamental groups
Galois cover
braid monodromy factorization

Access to Document

10.1007/s10114-020-9220-9

Cite this

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abstract = "As known to all, it is quite difficult to compute the fundamental group of a surface of general type. In this paper, applying Moishezon-Teicher{\textquoteright}s algorithm, we investigate the fundamental group of a special surface of general type with zero topological index, namely, the Galois cover of the (2,3)-embedding of ℂℙ1 × T. Because the full presentation of the group is very complicated, we compute its special quotient and get an interesting result about its structure.",

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