Mathematics – Algebraic Geometry
Scientific paper
2004-05-30
Mathematics
Algebraic Geometry
Latex 12 pages; Typos fixed, Improved version of Theorem 1 with more discussions added
Scientific paper
The 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.
No associations
LandOfFree
On Branching Indices of Affine A-D-E Diagrams : A Geometrical Characterization by Kleinian Singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Branching Indices of Affine A-D-E Diagrams : A Geometrical Characterization by Kleinian Singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Branching Indices of Affine A-D-E Diagrams : A Geometrical Characterization by Kleinian Singularities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-34978