On fundamental groups related to degeneratable surfaces: conjectures and examples
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 3, pp. 565-603.

We argue that for a smooth surface S, considered as a ramified cover over ℂℙ 2 , branched over a nodal-cuspidal curve Bℂℙ 2 , one could use the structure of the fundamental group of the complement of the branch curve π 1 (ℂℙ 2 -B) to understand other properties of the surface and its degeneration and vice-versa. In this paper, we look at embedded-degeneratable surfaces — a class of surfaces admitting a planar degeneration with a few combinatorial conditions imposed on its degeneration. We close a conjecture of Teicher on the virtual solvability of π 1 (ℂℙ 2 -B) for these surfaces and present two new conjectures on the structure of this group, regarding non-embedded-degeneratable surfaces. We prove two theorems supporting our conjectures, and show that for ℂℙ 1 ×C g , where C g is a curve of genus g, π 1 (ℂℙ 2 -B) is a quotient of an Artin group associated to the degeneration.

Publié le :
Classification : 14D06, 14Q10, 14H20, 14H30, 20F36
Friedman, Michael 1 ; Teicher, Mina 1

1 Department of Mathematics Bar-Ilan University 52900 Ramat Gan, Israel
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Friedman, Michael; Teicher, Mina. On fundamental groups related to degeneratable surfaces: conjectures and examples. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 3, pp. 565-603. http://archive.numdam.org/item/ASNSP_2012_5_11_3_565_0/

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