Tropicalization of del Pezzo surfaces
| dc.contributor.author | Ren, Qingchun | |
| dc.contributor.author | Shaw, Kristin | |
| dc.contributor.author | Sturmfels, Bernd | |
| dc.date.accessioned | 2018-06-01T07:42:06Z | |
| dc.date.available | 2018-06-01T07:42:06Z | |
| dc.date.issued | 2016-03-30 | |
| dc.description.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. | en |
| dc.identifier.issn | 0001-8708 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/7893 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-7054 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 514 Topologie | de |
| dc.subject.ddc | 516 Geometrie | de |
| dc.subject.other | tropical geometry | en |
| dc.subject.other | cubic surface | en |
| dc.subject.other | Cox ring | en |
| dc.subject.other | 27 lines | en |
| dc.subject.other | tropical modification | en |
| dc.subject.other | tropical basis | en |
| dc.subject.other | hyperplane arrangement | en |
| dc.subject.other | Weyl group | en |
| dc.subject.other | polyhedral fan | en |
| dc.title | Tropicalization of del Pezzo surfaces | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.1016/j.aim.2016.03.017 | en |
| dcterms.bibliographicCitation.journaltitle | Advances in Mathematics | en |
| dcterms.bibliographicCitation.originalpublishername | Elsevier | en |
| dcterms.bibliographicCitation.originalpublisherplace | Amsterdam | en |
| dcterms.bibliographicCitation.pageend | 189 | en |
| dcterms.bibliographicCitation.pagestart | 156 | en |
| dcterms.bibliographicCitation.volume | 300 | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Diskrete Mathematik / Geometrie | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Diskrete Mathematik / Geometrie | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |