Communications in Number Theory and Physics

Volume 12 (2018)

Number 3

Local curves, wild character varieties, and degenerations

Pages: 491 – 542



Duiliu-Emanuel Diaconescu (High Energy Theory Group, Department of Physics & Astronomy, Rutgers University, Piscataway, New Jersey, U.S.A.)


Conjectural results for cohomological invariants of wild character varieties are obtained by counting curves in degenerate Calabi–Yau threefolds. A conjectural formula for $E$-polynomials is derived from the Gromov–Witten theory of local Calabi–Yau threefolds with normal crossing singularities. A refinement is also conjectured, generalizing existing results of Hausel, Mereb and Wong as well as recent joint work of Donagi, Pantev and the author for weighted Poincaré polynomials of wild character varieties.

Received 1 June 2017

Accepted 19 August 2017

Published 25 September 2018