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.
Classification: 14D06, 14Q10, 14H20, 14H30, 20F36
@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}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {3}, year = {2012}, pages = {565-603}, zbl = {1298.14015}, mrnumber = {3059838}, language = {en}, url = {http://www.numdam.org/item/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://www.numdam.org/item/ASNSP_2012_5_11_3_565_0/
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