LEADER 03840nam 2200577 450 001 9910788900203321 005 20220901065025.0 010 $a1-4704-0940-2 035 $a(CKB)3360000000464281 035 $a(EBL)3113321 035 $a(SSID)ssj0000893456 035 $a(PQKBManifestationID)11478647 035 $a(PQKBTitleCode)TC0000893456 035 $a(PQKBWorkID)10906105 035 $a(PQKB)10608989 035 $a(MiAaPQ)EBC3113321 035 $a(RPAM)17664677 035 $a(PPN)197102328 035 $a(EXLCZ)993360000000464281 100 $a20140613h20132013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAlgebraic and combinatorial aspects of tropical geometry $eCIEM Workshop on Tropical Geometry, December 12-16, 2011, International Center for Mathematical Meetings, Castro Urdiales, Spain /$fErwan Brugalle? [and four others],editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2013. 210 4$dİ2013 215 $a1 online resource (362 p.) 225 1 $aContemporary mathematics,$x1098-3627 ;$v589$x0271-4132 300 $aDescription based upon print version of record. 311 $a0-8218-9146-4 320 $aIncludes bibliographical references. 327 $aDedication -- Preface -- Intersection multiplicity numbers between tropical hypersurfaces -- Introduction -- 1. Toric hypersurfaces -- 2. Intersection of toric hypersurfaces -- 3. Tropical hypersurfaces -- 4. Intersection of tropical hypersurfaces -- 5. Intersection multiplicity numbers between tropical hypersurfaces -- 6. Tropical intersection numbers via volumes of Cayley polytopes -- 7. Non degenerate tropical complete intersections -- References -- On the total curvature of tropical hypersurfaces -- 1. Introduction -- 2. Preliminary -- 2.1. Total curvature -- 2.2. Tropical hypersurfaces -- 2.3. Real convergent Puiseux series and tropicalisation -- 2.4. Real tropical hypersurfaces -- 3. Total curvature of real and complex amoebas -- 4. Complex and real total curvature of tropical hypersurfaces -- 4.1. Complex total curvature -- 4.2. Total curvature of real tropical hypersurfaces -- 5. Polyhedral total curvature of a real tropical hypersurface. -- 5.1. Definition and elementary properties -- 5.2. Elementary simplex case -- 5.3. Proof of Proposition 5.8 -- 6. Complement -- 6.1. Tropical lower bound -- Tropically unirational varieties -- 1. Tropical Unirationality -- Acknowledgements -- 2. Linear spaces, toric varieties, homogenisation, curves -- 3. Combining reparameterisations -- 4. Birational projections -- 5. Very local reparameterisations -- 6. Concluding remarks -- References -- A Guide to Tropicalizations -- 1. Introduction -- 2. Analytification -- 3. Tropicalization -- 4. Models over the valuation ring and reduction -- 5. Initial degeneration -- 6. Affine toric schemes over a valuation ring -- 7. Toric schemes over a valuation ring -- 6. The layered categories and the corresponding tropicalization functors. 410 0$aContemporary mathematics (American Mathematical Society).$v589$x0271-4132 606 $aTropical geometry$vCongresses 606 $aCombinatorial analysis$vCongresses 615 0$aTropical geometry 615 0$aCombinatorial analysis 676 $a516.3/5 686 $a14T05$a14T99$a51M20$a12J20$a14M25$a32P05$a14C30$a05E45$a14H52$a32S05$2msc 702 $aBrugalle?$b Erwan$f1977- 712 02$aCIEM (Universidad de Cantabria), 712 12$aCIEM Workshop on Tropical Geometry 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788900203321 996 $aAlgebraic and combinatorial aspects of tropical geometry$9833085 997 $aUNINA