LEADER 01349nam0 2200277 i 450 001 SUN0024368 005 20160621103125.516 010 $a08-218-2491-0$d0.00 100 $a20040921d1990 |0engc50 ba 101 $aeng 102 $aUS 105 $a|||| ||||| 200 1 $aPositive definite unimodular lattices with trivial automorphism groups$fEtsuko Bannai 210 $aProvidence$cAmerican mathematical society$d1990 215 $aIV, 70 p.$d26 cm. 410 1$1001SUN0024370$12001 $aMemoirs of the American Mathematical Society$v429$1210 $aProvidence$cAmerican mathematical society. 606 $a06-XX$xOrder, lattices, ordered algebraic structures [MSC 2020]$2MF$3SUNC019973 620 $aUS$dProvidence$3SUNL000273 700 1$aBannai$b, Etsuko$3SUNV020402$0728666 712 $aAmerican mathematical society$3SUNV001080$4650 801 $aIT$bSOL$c20200727$gRICA 856 4 $u/sebina/repository/catalogazione/documenti/Bannai - Positive definite unimodular lattices with trivial automorphism groups.pdf$zContents 912 $aSUN0024368 950 $aUFFICIO DI BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08PREST 06-XX 0251 $e08 5061 I 20040921 996 $aPositive definite unimodular lattices with trivial automorphism groups$91432803 997 $aUNICAMPANIA LEADER 01818nam 2200601 450 001 9910827839003321 005 20230803202256.0 010 $a0-87417-942-4 035 $a(CKB)3710000000104778 035 $a(EBL)4312875 035 $a(SSID)ssj0001195394 035 $a(PQKBManifestationID)11709061 035 $a(PQKBTitleCode)TC0001195394 035 $a(PQKBWorkID)11161952 035 $a(PQKB)10033741 035 $a(MiAaPQ)EBC4312875 035 $a(OCoLC)877908083 035 $a(MdBmJHUP)muse32928 035 $a(Au-PeEL)EBL4312875 035 $a(CaPaEBR)ebr11139254 035 $a(EXLCZ)993710000000104778 100 $a20160119h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe essential eldercare handbook for Nevada /$fKim Boyer and Mary Shapiro ; design by Kathleen Szawiola 210 1$aReno, Nevada ;$aLas Vegas, [Nevada] :$cUniversity of Nevada Press,$d2014. 210 4$dİ2014 215 $a1 online resource (141 p.) 300 $aIncludes index. 311 $a0-87417-941-6 320 $aIncludes bibliographical references and index. 606 $aOlder people$xCare$zNevada 606 $aCaregivers$zNevada 606 $aLong-term care facilities$zNevada 606 $aEstate planning$zNevada 615 0$aOlder people$xCare 615 0$aCaregivers 615 0$aLong-term care facilities 615 0$aEstate planning 676 $a362.609793 700 $aBoyer$b Kim$f1965-$01655135 702 $aShapiro$b Mary$f1949- 702 $aSzawiola$b Kathleen 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827839003321 996 $aThe essential eldercare handbook for Nevada$94007386 997 $aUNINA LEADER 05438nam 22006253 450 001 9910970819103321 005 20231110230425.0 010 $a9781470465346 010 $a1470465345 035 $a(CKB)4100000011975798 035 $a(MiAaPQ)EBC6661102 035 $a(Au-PeEL)EBL6661102 035 $a(OCoLC)1259591042 035 $a(RPAM)22488291 035 $a(EXLCZ)994100000011975798 100 $a20210901d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEffective Faithful Tropicalizations Associated to Linear Systems on Curves 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$dİ2021. 215 $a1 online resource (122 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.270 311 08$a9781470447533 311 08$a1470447533 320 $aIncludes bibliographical references and index. 327 $aCover -- 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 ?-metric graphs -- 3.3. Weighted ?-metric graphs -- 3.4. Skeleton as a weighted ?-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]. 327 $aChapter 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. 330 $a"For a connected smooth projective curve of genus g, global sections of any line bundle L with deg(L) 2g 1 give an embedding of the curve into projective space. We consider an analogous statement for a Berkovich skeleton in nonarchimedean geometry: We replace projective space by tropical projective space, and an embedding by a homeomorphism onto its image preserving integral structures (or equivalently, since is a curve, an isometry), which is called a faithful tropicalization. Let be an algebraically closed field which is complete with respect to a nontrivial nonarchimedean value. Suppose that is defined over and has genus g 2 and that is a skeleton (that is allowed to have ends) of the analytification an of in the sense of Berkovich. We show that if deg(L) 3g 1, then global sections of L give a faithful tropicalization of into tropical projective space. As an application, when Y is a suitable affine curve, we describe the analytification Y an as the limit of tropicalizations of an effectively bounded degree"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aGeometry, Algebraic 606 $aTropical geometry 606 $aAlgebraic geometry -- Tropical geometry -- Tropical geometry$2msc 606 $aAlgebraic geometry -- Arithmetic problems. Diophantine geometry -- Rigid analytic geometry$2msc 606 $aAlgebraic geometry -- Cycles and subschemes -- Divisors, linear systems, invertible sheaves$2msc 615 0$aGeometry, Algebraic. 615 0$aTropical geometry. 615 7$aAlgebraic geometry -- Tropical geometry -- Tropical geometry. 615 7$aAlgebraic geometry -- Arithmetic problems. Diophantine geometry -- Rigid analytic geometry. 615 7$aAlgebraic geometry -- Cycles and subschemes -- Divisors, linear systems, invertible sheaves. 676 $a516.3/52 686 $a14T05$a14G22$a14C20$2msc 700 $aKawaguchi$b Shu$01799882 701 $aYamaki$b Kazuhiko$01799883 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910970819103321 996 $aEffective Faithful Tropicalizations Associated to Linear Systems on Curves$94344303 997 $aUNINA