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Theta characteristics of tropical \(K_4\)-curves. (English) Zbl 1390.14195
Smith, Gregory G. (ed.) et al., Combinatorial algebraic geometry. Selected papers from the 2016 apprenticeship program, Ottawa, Canada, July–December 2016. Toronto: The Fields Institute for Research in the Mathematical Sciences; New York, NY: Springer (ISBN 978-1-4939-7485-6/hbk; 978-1-4939-7486-3/ebook). Fields Institute Communications 80, 65-86 (2017).
Summary: A \(K_4\)-curve is a smooth proper curve \(X\) of genus 3 over a field with valuation whose Berkovich skeleton \(\Gamma\) is a complete graph on four vertices. The curve \(X\) has 28 effective theta characteristics – the 28 bitangents to a canonical embedding – while \(\Gamma\) has exactly seven effective tropical theta characteristics, as shown by Zharkov. We prove that the 28 effective theta characteristics of a \(K_4\)-curve specialize to the theta characteristics of its minimal skeleton in seven groups of four.
For the entire collection see [Zbl 1387.14014].

14T05 Tropical geometry (MSC2010)
14C20 Divisors, linear systems, invertible sheaves
14H45 Special algebraic curves and curves of low genus
14H50 Plane and space curves
14G22 Rigid analytic geometry
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