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1998-08-17Buch DOI: 10.18452/2681
Picard-Einstein Metrics and Class Fields Connected with Apollonius Cycle
dc.contributor.authorHolzapfel, Rolf-Peter
dc.date.accessioned2017-06-15T17:57:41Z
dc.date.available2017-06-15T17:57:41Z
dc.date.created2005-11-15
dc.date.issued1998-08-17none
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3333
dc.description.abstractWe define Picard_Einstein metrics on complex algebraic surfaces as Kähler-Einstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along cycles. We demonstrate how the tool of orbital heights, especially the Proportionality Theorem presented in [H98], works for detecting such orbital cycles on the projective plane. The simplest cycle we found on this way is supported by a quadric and three tangent lines (Apollonius configuration). We give a complete proof for the fact that it belongs to the congruence subgroup of level 1 + i of the full Picard modular group of Gauß numbers together with precise octahedral- symmetric interpretation as moduli space of an explicit Shimura family of curves of genus 3. Proofs are based only on the Proportionality Theorem and classification results for hermitian lattices and algebraic surfaces.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.relation.ispartofseriesPreprints aus dem Institut für Mathematik - 15, Mathematik-Preprints, ISSN:0863-0976
dc.subjectunit balleng
dc.subjectKähler-Einstein metriceng
dc.subjectarithmetic groupeng
dc.subjectPicard modular groupeng
dc.subjectnegative constant curvatureeng
dc.subjectalgebraic curveseng
dc.subjectmoduli spaceeng
dc.subjectShimura surfaceeng
dc.subjectGauß latticeeng
dc.subject.ddc510 Mathematik
dc.titlePicard-Einstein Metrics and Class Fields Connected with Apollonius Cycle
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10053551
dc.identifier.doihttp://dx.doi.org/10.18452/2681
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.container-titleMathematik-Preprints
local.edoc.container-issn0863-0976
local.edoc.pages63
local.z-edoc.journal-periodikumAusgabe15,
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume1998
local.edoc.container-issue15
local.edoc.container-year1998

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