Effective Faithful Tropicalizations Associated to Linear Systems on Curves

Kawaguchi Yamaki

ISBN 10: 1470447533 / ISBN 13: 9781470447533

Published by American Mathematical Society

2021. paperback. . . . . . Books ship from the US and Ireland. Seller Inventory # V9781470447533

Synopsis:

"For a connected smooth projective curve 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 is a curve, an isometry), which is called a faithful tropicalization. Let be an algebraically closed field which is complete with respect to a nontrivial nonarchimedean value. Suppose that is defined over and has genus g 2 and that is a skeleton (that is allowed to have ends) of the analytification an of in the sense of Berkovich. We show that if deg(L) 3g 1, then global sections of L give a faithful tropicalization of 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"--

Bibliographic Details

Title: Effective Faithful Tropicalizations ...
Publisher: American Mathematical Society
Binding: Soft cover
Condition: New