Chennai Mathematical Institute


3:30 p.m,
Meeting ID: 885 6373 1662, Passcode: 662471
Transversality and symmetry for pseudoholomorphic covers

Paramjit Singh
Humboldt University of Berlin.


Moduli spaces of simple (or somewhere injective in the closed setting) pseudoholomorphic curves arise as smooth manifolds. In this talk, we present some ideas for the multiply covered case. That is the question of equivariant transversality – do generic equivariant sections of an orbi-bundle intersect the zero section transversally? In particular, we outline results like unbranched multiple covers of closed curves are generically regular and simple index 0 curves in dimension greater than four are generically super-rigid. We also indicate some partial results for regularity of branched covers, using a stratification argument for spaces of multiple covers, framed in terms of a representation-theoretic splitting of Cauchy Riemann operators with symmetries.

This talk is based on Wendl’s paper “Transversality and super-rigidity for multiply covered holomorphic curves” (arXiv:1609.09867).