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Lifting tropical self intersections. (English) Zbl 1441.14205
Tropical geometry is a combinatorially effective tool, which can be viewed as a piecewise-linear shadow classical algebraic geometry. In the article under review, the tropicalizations of intersections of plane curves are studied, focusing on the case where two plane curves have the same tropicalization. For a comprehensive study of tropical divisors see [M. Baker and D. Jensen, in: Nonarchimedean and tropical geometry. Based on two Simons symposia, Island of St. John, March 31 – April 6, 2013 and Puerto Rico, February 1–7, 2015. Cham: Springer. 365–433 (2016; Zbl 1349.14193)].
The main result of the article shows that tropical divisors arising as such intersections form a polyhedral complex, and the author computes the dimension of this complex. Specializing to the case when the genus is at most \(1\), it is also shown that a large class of divisors satisfying certain combinatorial criteria are realisable.

MSC:
14T15 Combinatorial aspects of tropical varieties
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References:
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