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Mixed tête-à-tête twists as monodromies associated with holomorphic function germs

Geometriae Dedicata volume 210, pages 43–64 (2021)Cite this article

Abstract

Tête-à-tête graphs were introduced by N. A’Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed tête-à-tête graphs provide a generalization which define mixed tête-à-tête twists, which are pseudo-periodic automorphisms on surfaces. We characterize the mixed tête-à-tête twists as those pseudo-periodic automorphisms that have a power which is a product of right-handed Dehn twists around disjoint simple closed curves, including all boundary components. It follows that the class of tête-à-tête twists coincides with that of monodromies associated with reduced function germs on isolated complex surface singularities.

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Authors and Affiliations

  1. Centro de Investigacion en Matematicas AC Guanajuato, Guanajuato, Mexico

    Pablo Portilla Cuadrado

  2. Unidad Cuernavaca del Instituto de Matemáticas, UNAM, Morelos, México

    Baldur Sigurðsson

Authors
  1. Pablo Portilla Cuadrado
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  2. Baldur Sigurðsson
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Correspondence to Pablo Portilla Cuadrado.

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P. Portilla: supported by SVP-2013-067644 Severo Ochoa FPI grant and by project by MTM2013-45710-C2-2-P, the two of them by the Spanish Ministry of Economy and Competitiveness MINECO; also supported by the project ERCEA 615655 NMST Consolidator Grant.

B. Sigurðsson is supported by the ERCEA 615655 NMST Consolidator Grant, by the Basque Government through the BERC 2014-2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.

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Portilla Cuadrado, P., Sigurðsson, B. Mixed tête-à-tête twists as monodromies associated with holomorphic function germs. Geom Dedicata 210, 43–64 (2021). https://doi.org/10.1007/s10711-020-00533-7

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  • DOI: https://doi.org/10.1007/s10711-020-00533-7

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