Mixed t\^ete-\`a-t\^ete twists as monodromies associated with holomorphic function germs

Pablo Portilla Cuadrado; Baldur Sigurðsson

doi:10.1007/s10711-020-00533-7

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arXiv · 1712.05988

Mixed t\^ete-\`a-t\^ete twists as monodromies associated with holomorphic function germs

Pablo Portilla Cuadrado·Baldur Sigurðsson

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Abstract

T\^ete-\`a-t\^ete graphs were introduced by N. A'Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed t\^ete-\`a-t\^ete graphs provide a generalization which define mixed t\^ete-\`a-t\^ete twists, which are pseudo-periodic automorphisms on surfaces. We characterize the mixed t\^ete-\`a-t\^ete 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 t\^ete-\`a-t\^ete twists coincides with that of monodromies associated with reduced function germs on isolated complex surface singularities.

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BibTeX RIS

Pablo Portilla Cuadrado, Baldur Sigurðsson. 2017-12-16. Mixed t\^ete-\`a-t\^ete twists as monodromies associated with holomorphic function germs. https://doi.org/10.1007/s10711-020-00533-7

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