Effective Faithful Tropicalizations Associated To Linear Systems On Curves
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Author | : Shu Kawaguchi |
Publisher | : |
Total Pages | : 122 |
Release | : 2021 |
Genre | : Linear systems |
ISBN | : 9781470465346 |
Download Effective Faithful Tropicalizations Associated to Linear Systems on Curves Book in PDF, Epub and Kindle
Author | : Shu Kawaguchi |
Publisher | : American Mathematical Soc. |
Total Pages | : 110 |
Release | : 2021-07-21 |
Genre | : Education |
ISBN | : 1470447533 |
Download Effective Faithful Tropicalizations Associated to Linear Systems on Curves Book in PDF, Epub and Kindle
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 |
Total Pages | : 142 |
Release | : 2022-05-24 |
Genre | : Mathematics |
ISBN | : 1470452286 |
Download The Canonical Ring of a Stacky Curve Book in PDF, Epub and Kindle
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Author | : Mark Gross |
Publisher | : American Mathematical Society |
Total Pages | : 122 |
Release | : 2022-07-18 |
Genre | : Mathematics |
ISBN | : 1470452979 |
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Author | : Stefan Geiss |
Publisher | : American Mathematical Society |
Total Pages | : 112 |
Release | : 2021-11-16 |
Genre | : Mathematics |
ISBN | : 1470449358 |
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Author | : Nuno Freitas |
Publisher | : American Mathematical Society |
Total Pages | : 105 |
Release | : 2022-05-24 |
Genre | : Mathematics |
ISBN | : 1470452103 |
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Author | : Zhiwu Lin |
Publisher | : American Mathematical Society |
Total Pages | : 136 |
Release | : 2022-02-02 |
Genre | : Mathematics |
ISBN | : 1470450445 |
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Author | : H. Flenner |
Publisher | : American Mathematical Society |
Total Pages | : 124 |
Release | : 2022-07-18 |
Genre | : Mathematics |
ISBN | : 1470453738 |
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Author | : Michele D’Adderio |
Publisher | : American Mathematical Society |
Total Pages | : 138 |
Release | : 2022-07-18 |
Genre | : Mathematics |
ISBN | : 1470471574 |
Download Decorated Dyck Paths, Polyominoes, and the Delta Conjecture Book in PDF, Epub and Kindle
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Author | : Camille Laurent |
Publisher | : American Mathematical Society |
Total Pages | : 108 |
Release | : 2022-04-08 |
Genre | : Mathematics |
ISBN | : 1470451387 |
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