Algebraic and Geometric Isomonodromic Deformations
نویسندگان
چکیده
منابع مشابه
Algebraic and Geometric Isomonodromic Deformations
Using the Gauss-Manin connection (Picard-Fuchs differential equation) and a result of Malgrange, a special class of algebraic solutions to isomonodromic deformation equations, the geometric isomonodromic deformations, is defined from “families of families” of algebraic varieties. Geometric isomonodromic deformations arise naturally from combinatorial strata in the moduli spaces of elliptic surf...
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Here we solve N × N Riemann-Hilbert (inverse monodromy) problems with all monodromy matrices having the structure of matrices of quasi-permutation (i.e. matrices which have only one non-zero element in each column and each row). Such RiemannHilbert problem may be associated to arbitrary Hurwitz space of algebraic curves L of genus g realized as N -sheeted covering over CP1, and allowes solution...
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“A`−1” stands for the A`−1 root system that underlies this model. Similarly, an elliptic Calogero-Moser system can be defined for each irreducible (but not necessary reduced) root system. Furthermore, for non-simply laced root systems, a kind of variants called “twisted model” and “extended twisted models” are also known. Those elliptic Calogero-Moser systems are known to possess an isospectral...
متن کاملSchlesinger transformations for elliptic isomonodromic deformations
Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system’s tau-function is computed and we obtain an explicit expression for the ratio of the old and ...
متن کاملOn the Geometry of Isomonodromic Deformations
This note examines the geometry behind the Hamiltonian structure of isomonodromy deformations of connections on vector bundles over Riemann surfaces. The main point is that one should think of an open set of the moduli of pairs (V,∇) of vector bundles and connections as being obtained by “twists” supported over points of a fixed vector bundle V0 with a fixed connection ∇0; this gives two deform...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2001
ISSN: 0022-040X
DOI: 10.4310/jdg/1090349280