1.

Record Nr.

UNINA9910827839003321

Autore

Boyer Kim <1965->

Titolo

The essential eldercare handbook for Nevada / / Kim Boyer and Mary Shapiro ; design by Kathleen Szawiola

Pubbl/distr/stampa

Reno, Nevada ; ; Las Vegas, [Nevada] : , : University of Nevada Press, , 2014

©2014

ISBN

0-87417-942-4

Descrizione fisica

1 online resource (141 p.)

Disciplina

362.609793

Soggetti

Older people - Care - Nevada

Caregivers - Nevada

Long-term care facilities - Nevada

Estate planning - Nevada

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Includes index.

Nota di bibliografia

Includes bibliographical references and index.



2.

Record Nr.

UNINA9910970819103321

Autore

Kawaguchi Shu

Titolo

Effective Faithful Tropicalizations Associated to Linear Systems on Curves

Pubbl/distr/stampa

Providence : , : American Mathematical Society, , 2021

©2021

ISBN

9781470465346

1470465345

Edizione

[1st ed.]

Descrizione fisica

1 online resource (122 pages)

Collana

Memoirs of the American Mathematical Society ; ; v.270

Classificazione

14T0514G2214C20

Altri autori (Persone)

YamakiKazuhiko

Disciplina

516.3/52

Soggetti

Geometry, Algebraic

Tropical geometry

Algebraic geometry -- Tropical geometry -- Tropical geometry

Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rigid analytic geometry

Algebraic geometry -- Cycles and subschemes -- Divisors, linear systems, invertible sheaves

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Cover -- Title page -- Chapter 1. Introduction -- Notation and Conventions -- Chapter 2. Preliminaries -- 2.1. Semistable models and semistable pairs -- 2.2. Berkovich spaces -- 2.3. Skeleta associated to strictly semistable models -- 2.4. Skeleta associated to strictly semistable pairs -- 2.5. Some properties of skeleta -- 2.6. Tropical geometry -- 2.7. Faithful tropicalization -- Chapter 3. Good models -- 3.1. Good models of -- 3.2. Theory of divisors on Λ-metric graphs -- 3.3. Weighted Λ-metric graphs -- 3.4. Skeleton as a weighted Λ-metric graph (with a finite graph structure) -- 3.5. Construction of a model of (  ,  ) -- Chapter 4. Unimodular tropicalization of minimal skeleta for   ≥2 -- 4.1. Useful lemmas -- 4.2. Fundamental vertical divisors -- 4.3. Stepwise vertical divisors -- 4.4. Edge-base sections and edge-unimodularity sections -- 4.5. Unimodular tropicalization -- Chapter 5. Faithful tropicalization of minimal skeleta for   ≥2 -- Notation and terminology of Chapter 5 -- 5.1. Separating points on an edge of



connected type -- 5.2. Separating points in different edges -- 5.3. Separating vertices -- 5.4. Faithful tropicalization of the minimal skeleton -- Chapter 6. Faithful tropicalization of minimal skeleta in low genera -- 6.1. Genus 0 case -- 6.2. Genus 1 case -- Chapter 7. Faithful tropicalization of arbitrary skeleta -- Notation and terminology of Chapter 7 -- 7.1. Geodesic paths -- 7.2. Stepwise vertical divisor associated to a point in   (  ) -- 7.3. Base sections and   -unimodularity sections -- 7.4. Good model -- 7.5. Proof of Proposition 7.8 -- 7.6. Proof of Theorem 1.2 -- 7.7. Upper bound for the dimension of the target space -- Chapter 8. Complementary results -- 8.1. Theorem 1.2 is optimal for curves in low genera -- 8.2. A very ample line bundle that does not admit a faithful tropicalization -- 8.3. Comparison with [42].

Chapter 9. Limit of tropicalizations by polynomials of a bounded degree -- 9.1. Statement of the result -- 9.2. Polynomial of bounded degree that separates two points -- 9.3. Proof of Theorem 1.7 -- Bibliography -- Subject Index -- Symbol Index -- Back Cover.

Sommario/riassunto

"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"--