Macdonald formula for curves with planar singularities
By Davesh Maulik, Zhiwei Yun. 2011
58 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Pharmacology
View Paper: https://www.semanticscholar.org/paper/0e62799a2676e9c78cac0cc71004b5d2d020b225
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In Algebra and Number Theory
- Vivek V. Shende
- Jacob Rasmussen
- Alexei Oblomkov
- Junliang Shen
- Davesh Maulik
- E. Gorsky
- Tom H. Koornwinder
In Geometry and Topology
- Vivek V. Shende
- E. Gorsky
- Alexei Oblomkov
- Jacob Rasmussen
- Junliang Shen
- Davesh Maulik
- Peter S. Ozsv'ath
- Zolt'an Szab'o
In Pharmacology
Citations in the corpus
- Torus knots and the rational DAHA (2012, background): “termediate extensions of their restrictions to Ars. This fact is established for f ∗CMf by Yun [Yun11], and a combination of the arguments there with the appropriate Sn enrichment of the arguments in [MY11] yields the result for h∗f∗CHe (see [OY??] for details). Thus we conclude: Theorem 9.5. Let th”
- Cohomological χ–independence for moduli of one-dimensional sheaves and moduli of Higgs bundles (2020, background): “After that, support theorems become powerful tools in various branches of mathematics; see for example [4, 7, 32, 33, 40, 51, 52].”
- The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link (2012, methodology): “For the Jacobians this follows from Ngô’s support theorem [53]; the geometric content of [49; 51] was to establish the same for the Hilbert schemes.”