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010 a| 2022007713;

020 a| 9781470447533q| (paperback);

020 z| 9781470465346q| (epub);

035 a| (WaSeSS)ssj0002593480;

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100 1 a| Kawaguchi, Shu.?| UNAUTHORIZED;

245 10 a| Effective faithful tropicalizations associated to linear systems on curvesh| [electronic resource] /c| Shu Kawaguchi, Kazuhiko Yamaki.;

260 a| Providence :b| American Mathematical Society,c| [2021];

300 a| v, 110 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 270, Number 1323 (seventh of 7 numbers);

504 a| Includes bibliographical references and index.;

506 a| Available only to authorized users.;

520 a| "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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Geometry, Algebraic.=| ^A42380;

650 0 a| Tropical geometry.=| ^A1266644;

650 7 a| Algebraic geometry -- Tropical geometry -- Tropical geometry.2| msc;

650 7 a| Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rigid analytic geometry.2| msc;

650 7 a| Algebraic geometry -- Cycles and subschemes -- Divisors, linear systems, invertible sheaves.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Yamaki, Kazuhiko.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6661102;

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Effective faithful tropicalizations associated to linear systems on curves / Shu Kawaguchi, Kazuhiko Yamaki.

Author/creator	Kawaguchi, Shu
Other author	Yamaki, Kazuhiko.
Format	Electronic
Publication Info	Providence : American Mathematical Society, [2021]
Description	v, 110 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Geometry, Algebraic. Tropical geometry.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 270, Number 1323 (seventh of 7 numbers)
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022007713
ISBN	9781470447533 (paperback)
ISBN	(epub)

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Effective faithful tropicalizations associated to linear systems on curves / Shu Kawaguchi, Kazuhiko Yamaki.

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