Journal Article

Lagrangian Fibrations in Duality on Moduli Spaces of Rank 2 Logarithmic Connections Over the Projective Line

Frank Loray and Masa-Hiko Saito

in International Mathematics Research Notices

Volume 2015, issue 4, pages 995-1043
Published in print January 2015 | ISSN: 1073-7928
Published online October 2013 | e-ISSN: 1687-0247 | DOI: http://dx.doi.org/10.1093/imrn/rnt232
Lagrangian Fibrations in Duality on Moduli Spaces of Rank 2 Logarithmic Connections Over the Projective Line

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We study the moduli space of logarithmic connections of rank 2 on minus n points with fixed spectral data. There are two natural Lagrangian maps: one toward apparent singularities of the associated Fuchsian scalar equation and another one toward moduli of parabolic bundles. We show that these are transversal and dual to each other. In case n=5, we recover the beautiful geometry of Del Pezzo surfaces of degree 4.

Journal Article.  12358 words.  Illustrated.

Subjects: Mathematics

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