Download or read book Effective Faithful Tropicalizations Associated to Linear Systems on Curves written by Shu Kawaguchi and published by . This book was released on 2021 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Effective Faithful Tropicalizations Associated to Linear Systems on Curves written by Shu Kawaguchi and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Canonical Ring of a Stacky Curve written by John Voight and published by American Mathematical Society. This book was released on 2022-05-24 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

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Download or read book Isoperimetric Inequalities in Unbounded Convex Bodies written by Gian Paolo Leonardi and published by American Mathematical Society. This book was released on 2022-04-08 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.