Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-7054
Main Title: Tropicalization of del Pezzo surfaces
Author(s): Ren, Qingchun
Shaw, Kristin
Sturmfels, Bernd
Type: Article
Language Code: en
Abstract: We determine the tropicalizations of very affine surfaces over a valued field that are obtained from del Pezzo surfaces of degree 5, 4 and 3 by removing their (-1)-curves. On these tropical surfaces, the boundary divisors are represented by trees at infinity. These trees are glued together according to the Petersen, Clebsch and Schläfli graphs, respectively. There are 27 trees on each tropical cubic surface, attached to a bounded complex with up to 73 polygons. The maximal cones in the 4-dimensional moduli fan reveal two generic types of such surfaces.
URI: https://depositonce.tu-berlin.de//handle/11303/7893
http://dx.doi.org/10.14279/depositonce-7054
Issue Date: 30-Mar-2016
Date Available: 1-Jun-2018
DDC Class: 514 Topologie
516 Geometrie
Subject(s): tropical geometry
cubic surface
Cox ring
27 lines
tropical modification
tropical basis
hyperplane arrangement
Weyl group
polyhedral fan
License: http://rightsstatements.org/vocab/InC/1.0/
Journal Title: Advances in Mathematics
Publisher: Elsevier
Publisher Place: Amsterdam
Volume: 300
Publisher DOI: 10.1016/j.aim.2016.03.017
Page Start: 156
Page End: 189
ISSN: 0001-8708
Appears in Collections:FG Diskrete Mathematik / Geometrie » Publications

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