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Effective Faithful Tropicalizations Associated to Linear Systems on Curves

Author: Shu Kawaguchi
Publisher:
ISBN: 9781470465346
Category : Linear systems
Languages : en
Pages : 122

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Book Description

Effective Faithful Tropicalizations Associated to Linear Systems on Curves

Author: Shu Kawaguchi
Publisher:
ISBN: 9781470465346
Category : Linear systems
Languages : en
Pages : 122

Get Book

Book Description

Effective Faithful Tropicalizations Associated to Linear Systems on Curves

Author: Shu Kawaguchi
Publisher: American Mathematical Soc.
ISBN: 1470447533
Category : Education
Languages : en
Pages : 110

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Book Description
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.

The Canonical Ring of a Stacky Curve

Author: John Voight
Publisher: American Mathematical Society
ISBN: 1470452286
Category : Mathematics
Languages : en
Pages : 142

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