On Branching Indices of Affine A-D-E Diagrams : A Geometrical Characterization by Kleinian Singularities

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dc.creatorRoan, Shi-shyr
dc.date2004-05-30
dc.date2004-10-07
dc.date.accessioned2026-07-07T05:08:44Z
dc.date.available2026-07-07T05:08:44Z
dc.descriptionThe exceptional configuration of the minimal resolution $\hat{S}_G $ of a Kleinian quotient surface $S_G (:= \CZ^2/G)$ is depicted by a $A$-$D$-$E$ Coxeter-Dynkin diagram. In this article, we show that branching indices of the affine $A$-$D$-$E$ diagram is geometrically characterized by a certain special function $F$ of $S_G$ as the multiplicities of its divisor components in $\hat{S}_G$, a version parallel to the elliptic fibration near certain types of simple singular fibers in Kodaira's elliptic surface theory. We further obtain the uniqueness property of the function $F$ (modular local units) among all local functions in $S_G$ near the singular point whose divisors in $\hat{S}_G $ display the affine $A$-$D$-$E$ diagram configuration.
dc.descriptionLatex 12 pages; Typos fixed, Improved version of Theorem 1 with more discussions added
dc.identifierhttps://arxiv.org/abs/math/0405580
dc.identifierhttp://arxiv.org/abs/math/0405580
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71382
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14J17, 14L30, 20C30, 32S25
dc.titleOn Branching Indices of Affine A-D-E Diagrams : A Geometrical Characterization by Kleinian Singularities
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