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Corpus ID: 54582801

Arithmetic and metric aspects of open de Rham spaces

@article{Hausel2018ArithmeticAM,
title={Arithmetic and metric aspects of open de Rham spaces},
author={Tam{\'a}s Hausel and M. L. Wong and Dimitri Wyss},
journal={arXiv: Algebraic Geometry},
year={2018}
}

In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincar\'e polynomial---of the open de Rham space, defined and studied by Boalch, of certain moduli of irregular meromorphic connections on the trivial bundle on $\mathbb{P}^1$. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild… CONTINUE READING