University of Maryland



Deligne pairings and holomorphic extension of analytic torsion


The purpose of this talk is to suggest an approach to certain constructions in hyperkähler geometry via Deligne pairings. I will discuss the concrete example of rank 1 Higgs bundles on a Riemann surface. The method produces a flat connection on a combination of determinant bundles over the de Rham moduli space. We show that the holomorphic extension of analytic torsion, introduced by Fay and used in this context by Hitchin, can be interpreted as a covariantly constant section of this bundle. The hyperholomorphic line bundle on the twistor space admits a meromorphic connection, and this also easily follows from this construction. This is joint work with Gerard Freixas i Montplet.


The Catalan Mathematical Society invites participants to this first congress of a biannual series focusing on current research topics across several areas of Mathematics.

Plenary talks and thematic sessions have been selected by the Scientific Committee of the SCM. Special thanks are due to the organisers of the thematic sessions and to the local mathematical community as a whole for their support to this congress.


Societat Catalana de Matemàtiques
Institut d'Estudis Catalans
Carrer del Carme, 47
08001 Barcelona

Phone: +34 933 248 583

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