We argue that for a smooth surface , considered as a ramified cover over , branched over a nodal-cuspidal curve , one could use the structure of the fundamental group of the complement of the branch curve 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 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 , where is a curve of genus , is a quotient of an Artin group associated to the degeneration.
@article{ASNSP_2012_5_11_3_565_0, author = {Friedman, Michael and Teicher, Mina}, title = {On fundamental groups related to degeneratable surfaces: conjectures and examples}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {565--603}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {3}, year = {2012}, mrnumber = {3059838}, zbl = {1298.14015}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_3_565_0/} }
TY - JOUR AU - Friedman, Michael AU - Teicher, Mina TI - On fundamental groups related to degeneratable surfaces: conjectures and examples JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 565 EP - 603 VL - 11 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_3_565_0/ LA - en ID - ASNSP_2012_5_11_3_565_0 ER -
%0 Journal Article %A Friedman, Michael %A Teicher, Mina %T On fundamental groups related to degeneratable surfaces: conjectures and examples %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 565-603 %V 11 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_3_565_0/ %G en %F ASNSP_2012_5_11_3_565_0
Friedman, Michael; Teicher, Mina. On fundamental groups related to degeneratable surfaces: conjectures and examples. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 3, pp. 565-603. http://archive.numdam.org/item/ASNSP_2012_5_11_3_565_0/
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