Macdonald formula for curves with planar singularities

Details Macdonald formula for curves with planar singularities Macdonald formula for curves with planar singularities

2011-07-12

arxiv.org/abs/1107.2175v2

Mathematics

Algebraic Geometry

16 pages, comments welcome

Scientific paper

We generalize Macdonald's formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes to the cohomology of the compactified Jacobian of the curve. The new formula is a consequence of a stronger identity between certain perverse sheaves defined by a family of curves satisfying mild conditions. The proof makes an essential use of Ngo's support theorem for compactified Jacobians and generalizes this theorem to the relative Hilbert scheme of such families. As a consequence, we generalize part of the Weil conjectures to the Hilbert-zeta function of curves with planar singularities.

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