NDLI: Gérard–Levelt membranes

Content Provider	Springer Nature Link
Author	Corel, Eduardo
Copyright Year	2012
Abstract	We present an unexpected application of tropical convexity to the determination of invariants for linear systems of differential equations. We show that the classical Gérard–Levelt lattice saturation procedure can be geometrically understood in terms of a projection on the tropical linear space attached to a subset of the local affine Bruhat–Tits building, which we call the Gérard–Levelt membrane. This provides a way to compute the true Poincaré rank, but also the Katz rank of a meromorphic connection without having to perform either gauge transforms or ramifications of the variable. We finally present an efficient algorithm to compute this tropical projection map, generalising Ardila’s method for Bergman fans to the case of the tight-span of a valuated matroid.
Starting Page	757
Ending Page	776
Page Count	20
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	37
Issue Number	4
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2012-08-16
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Meromorphic connections Tropical convexity Valuated matroids Combinatorics Convex and Discrete Geometry Order, Lattices, Ordered Algebraic Structures Computer Science Group Theory and Generalizations
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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Gérard–Levelt membranes