2,190 research outputs found
The symplectic and twistor geometry of the general isomonodromic deformation problem
Hitchin's twistor treatment of Schlesinger's equations is extended to the
general isomonodromic deformation problem. It is shown that a generic linear
system of ordinary differential equations with gauge group SL(n,C) on a Riemann
surface X can be obtained by embedding X in a twistor space Z on which sl(n,C)
acts. When a certain obstruction vanishes, the isomonodromic deformations are
given by deforming X in Z. This is related to a description of the deformations
in terms of Hamiltonian flows on a symplectic manifold constructed from affine
orbits in the dual Lie algebra of a loop group.Comment: 35 pages, LATE
A note on the (1, 1,..., 1) monopole metric
Recently K. Lee, E.J. Weinberg and P. Yi in CU-TP-739, hep-th/9602167,
calculated the asymptotic metric on the moduli space of (1, 1, ..., 1) BPS
monopoles and conjectured that it was globally exact. I lend support to this
conjecture by showing that the metric on the corresponding space of Nahm data
is the same as the metric they calculate.Comment: 12 pages, latex, no figures, uses amsmath, amsthm, amsfont
Manifolds with holonomy U*(2m)
We consider the geometry determined by a torsion-free affine connection whose
holonomy lies in the subgroup U*(2m), a real form of GL(2m,C), otherwise
denoted by SL(m,H).U(1). We show in particular how examples may be generated
from quaternionic K\"ahler or hyperk\"ahler manifolds with a circle action.Comment: Based on the author's Santalo Lecture delivered in the Universidad
Complutense, Madrid on October 10th 2013. To appear in the Revista
Matem\'atica Complutens
The moduli space of special Lagrangian submanifolds
This paper considers the natural geometric structure on the moduli space of
deformations of a compact special Lagrangian submanifold of a Calabi-Yau
manifold. From the work of McLean this is a smooth manifold with a natural
metric. It is shown that the metric is induced from a local
Lagrangian immersion into the product of cohomology groups . Using this approach, an interpretation of the mirror symmetry
discussed by Strominger, Yau and Zaslow is given in terms of the classical
Legendre transform.Comment: 14 page
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