Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation

@inproceedings{Shende2011HilbertSO,
  title={Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation},
  author={Vivek V. Shende},
  year={2011}
}
Let C be a locally planar curve. Its versal deformation admits a stratification by the genera of the fibres. The strata are singular; we show that their multiplicities at the central point are determined by the Euler numbers of the Hilbert schemes of points on C. These Euler numbers have made two prior appearances. First, in certain simple cases, they control the contribution of C to the Pandharipande-Thomas curve counting invariants of threefolds. In this context, our result identifies the… CONTINUE READING