Seminario di algebra e geometria
ore
15:30
presso Seminario II
We consider the generating series of Euler numbers
of Hilbert schemes of points on a singular plane curve. After a change of variables, we show this counts the number of h-nodal
curves in deformations in nearby h-parameter families. Similar
arguments, made globally, lead to a proof of Gottsche's conjecture
on the universality of numbers of nodal curves on surfaces. Finally,
we conjecturally relate a refinement of this generating series
to the homological knot invariants of the links of the singularities.