Tropical geometry for Nagata's conjecture and Legendrian curves

Diplôme Thèse Tropical geometry for Nagata's conjecture and Legendrian curves eng 2015-12-08 author Kalinin Nikita 743425 director Mikhalkin Grigory 681622 10.13097/archive-ouverte/unige:80308 urn:nbn:ch:unige-803089 Sc. 4864 In this thesis, tropical methods in singularity theory and legendrian geometry are developed; tropical modifications are surveyed and several technical statements about them are proven. In more details, if a planar algebraic curve over a valuation field contains an $m$-fold point, then there is a certain collection of faces in the subdivision of the Newton polygon of this curve, with total area of order $m^2$. This estimate can be applied in Nagata's type questions for curves. Then, the notion of a tropical point of multiplicity $m$ is revisited. With some additional assumptions, the tropicalization of a complex legendrian curve in $mathbb CP^3$ is proven to enjoy a certain divisibility property. Finally, with help of tropical modifications, the tropical Weil reciprocity law is proven and several restrictions on the realizability of non-transversal intersection of tropical varieties are obtained. Tropical geometry Legendrian geometry Nagata's conjecture Singular points Tropical modifications Dewey 510 25 Section de mathématiques 11 false 845 Géométrie algébrique tropicale 3dc6777f-e43d-464e-ab70-f9267b79312f Thesis Public dissertation.pdf 2115550 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Tropical geometry for Nagata's conjecture and Legendrian curves				2015	1,237	789

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Kalinin, Nikita