MARC Record from harvard_bibliographic_metadata

LEADER: 02650cam a2200409Ii 4500
001 014142076-6
005 20140819100451.0
008 140611s2014 fr a b 001 0 eng d
016 7 $a016737613$2Uk
020 $a9782856297834 (pbk.)
020 $a2856297838 (pbk.)
035 0 $aocn881286870
040 $aHDC$cHDC$erda$dIQU$dUKMGB$dCOD$dYDXCP$dIPL$dOCLCF
041 0 $aeng$bfre
050 14 $aQA564$b.B795 2014
082 04 $a516.35$223
100 1 $aBurgos Gil, José I.$q(José Ignacio),$d1962-$eauthor.
245 10 $aArithmetic geometry of toric varieties :$bmetrics, measures and heights /$cJosé Ignacio Burgos Gil, Patrice Philippon, Martín Sombra.
264 1 $aParis :$bSociété Mathématique de France,$c2014.
300 $avi, 222 pages :$billustrations ;$c24 cm.
336 $atext$2rdacontent
337 $aunmediated$2rdamedia
338 $avolume$2rdacarrier
490 1 $aAstérisque,$x0303-1179 ;$v360
546 $aAbstract also in French.
504 $aIncludes bibliographical references (pages 207-212) and index.
505 0 $aMetrized line bundles and their associated heights -- The Legendre-Fenchel duality -- Toric varieties -- Metrics and measures on toric varieties -- Height of toric varieties -- Metrics from polytopes -- Variations on Fubini-Study metrics.
520 3 $aWe show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov geometry of toric varieties. In particular, we consider models over a discrete valuation ring, metrized line bundles, and their associated measures and heights. We show that these notions can be translated in terms of convex analysis, and are closely related to objects like polyhedral complexes, concave functions, real Monge-Ampère measures, and Legendre-Fenchel duality. We also present a closed formula for the integral over a polytope of a function of one variable composed with a linear form. This formula allows us to compute the height of toric varieties with respect to some interesting metrics arising from polytopes. We also compute the height of toric projective curves with respect to the Fubini-Study metric and the height of some toric bundles"--Page 4 of cover.
650 0 $aToric varieties.
650 0 $aArakelov theory.
650 7 $aArakelov theory.$2fast
650 7 $aToric varieties.$2fast
700 1 $aSombra, Martín,$d1970-$eauthor.
700 1 $aPhilippon, Patrice,$d1954-$eauthor.
830 0 $aAstérisque ;$v360.
988 $a20140819
906 $0OCLC