7 papers
Monodromy and vanishing cycles for sufficiently ample linear systems on simply connected surfaces
Ishan Banerjee, Nick Salter
We compute the mapping class group-valued monodromy of any sufficiently ample linear system on any smooth simply connected projective surface, identifying this with the r-spin mapp…
Fundamental groups of strata of abelian differentials of low codimension
Nick Salter
We show that for a stratum of projectivized abelian differentials with sufficiently many simple zeroes, the inclusion into the appropriate moduli space of pointed curves induces an…
Noninjectivity of the monodromy of certain equicritical strata
Peter Huxford, Nick Salter
An equicritical stratum is the locus of univariate monic squarefree complex polynomials where the critical points have prescribed multiplicities. Tracking the positions of both roo…
Topological monodromy kernels for fundamental groups of discriminant complements
Nick Salter
A linear system on a smooth complex algebraic surface gives rise to a family of smooth curves in the surface. Such a family has a topological monodromy representation valued in the…
Siegel-Veech Constants for Cyclic Covers of Generic Translation Surfaces
David Aulicino, Aaron Calderon, Carlos Matheus +2
We compute the asymptotic number of cylinders, weighted by their area to any non-negative power, on any cyclic branched cover of any generic translation surface in any stratum. Our…
Monodromy and vanishing cycles for complete intersection curves
Ishan Banerjee, Nick Salter
We compute the topological monodromy of every family of complete intersection curves. Like in the case of plane curves previously treated by the second-named author, we find the an…
Monodromy of stratified braid groups, II
Nick Salter
The space of monic squarefree polynomials has a stratification according to the multiplicities of the critical points, called the equicritical stratification. Tracking the position…