Advances in Theoretical and Mathematical Physics

Volume 24 (2020)

Number 8

The second of two special issues in honor of Cumrun Vafa’s 60th birthday

ADE Transform

Pages: 2043 – 2066

DOI: https://dx.doi.org/10.4310/ATMP.2020.v24.n8.a2

Authors

Ron Donagi (Department of Mathematics, University of Pennsylvania, Philadelphia, Pa., U.S.A.)

Martijn Wijnholt (Department of Mathematics, University of Pennsylvania, Philadelphia, Pa., U.S.A.)

Abstract

There is a beautiful correspondence between configurations of lines on a rational surface and tautological bundles over that surface.We extend this correspondence to families, by means of a generalized Fourier–Mukai transform that relates spectral data to bundles over a rational surface fibration.

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R.D. acknowledges partial support by NSF grant DMS-2001673 and by the Simons Foundation Collaboration grant No 390287 “Homological Mirror Symmetry.”

The research of M.W. was supported in part by a visiting faculty position at the mathematics department of the University of Pennsylvania.

Published 28 September 2021