Effective Faithful Tropicalizations Associated to Linear Systems on Curves
Author : Shu Kawaguchi
Publisher :
Page : 122 pages
File Size : 32,98 MB
Release : 2021
Category : Linear systems
ISBN : 9781470465346
Author : Shu Kawaguchi
Publisher :
Page : 122 pages
File Size : 32,98 MB
Release : 2021
Category : Linear systems
ISBN : 9781470465346
Author : Shu Kawaguchi
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 29,46 MB
Release : 2021-07-21
Category : Education
ISBN : 1470447533
For a connected smooth projective curve X of genus g, global sections of any line bundle L with deg(L) ≥ 2g + 1 give an embedding of the curve into projective space. We consider an analogous statement for a Berkovich skeleton in nonarchimedean geometry: We replace projective space by tropical projective space, and an embedding by a homeomorphism onto its image preserving integral structures (or equivalently, since X is a curve, an isometry), which is called a faithful tropicalization. Let K be an algebraically closed field which is complete with respect to a nontrivial nonarchimedean value. Suppose that X is defined over K and has genus g ≥ 2 and that Γ is a skeleton (that is allowed to have ends) of the analytification Xan of X in the sense of Berkovich. We show that if deg(L) ≥ 3g − 1, then global sections of L give a faithful tropicalization of Γ into tropical projective space. As an application, when Y is a suitable affine curve, we describe the analytification Y an as the limit of tropicalizations of an effectively bounded degree.
Author : John Voight
Publisher : American Mathematical Society
Page : 142 pages
File Size : 23,18 MB
Release : 2022-05-24
Category : Mathematics
ISBN : 1470452286
View the abstract.
Author : Mark Gross
Publisher : American Mathematical Society
Page : 122 pages
File Size : 42,1 MB
Release : 2022-07-18
Category : Mathematics
ISBN : 1470452979
View the abstract.
Author : Stefan Geiss
Publisher : American Mathematical Society
Page : 112 pages
File Size : 44,38 MB
Release : 2021-11-16
Category : Mathematics
ISBN : 1470449358
View the abstract.
Author : Nuno Freitas
Publisher : American Mathematical Society
Page : 105 pages
File Size : 12,61 MB
Release : 2022-05-24
Category : Mathematics
ISBN : 1470452103
View the abstract.
Author : Zhiwu Lin
Publisher : American Mathematical Society
Page : 136 pages
File Size : 16,23 MB
Release : 2022-02-02
Category : Mathematics
ISBN : 1470450445
View the abstract.
Author : H. Flenner
Publisher : American Mathematical Society
Page : 124 pages
File Size : 44,4 MB
Release : 2022-07-18
Category : Mathematics
ISBN : 1470453738
View the abstract.
Author : Michele D’Adderio
Publisher : American Mathematical Society
Page : 138 pages
File Size : 36,92 MB
Release : 2022-07-18
Category : Mathematics
ISBN : 1470471574
View the abstract.
Author : Camille Laurent
Publisher : American Mathematical Society
Page : 108 pages
File Size : 16,10 MB
Release : 2022-04-08
Category : Mathematics
ISBN : 1470451387
View the abstract.