Homology of Hilbert schemes of reducible locally planar curves

2017/11/17 by Oscar Kivinen, Kivinen, Oscar
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1711.06444

openalex publication_date 2017/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a complex, reduced, locally planar curve. We extend the results of Rennemo arXiv:1308.4104 to reducible curves by constructing an algebra A acting on V=\bigoplus_{n≥ 0} H_*(C^[n], ℚ), where C^[n] is the Hilbert scheme of n points on C. If m is the number of irreducible components of C, we realize A as a subalgebra of the Weyl algebra of \mathbbA^2m. We also compute the representation V in the simplest reducible example of a node.

Citations

• Khovanov-Rozansky homology and higher Catalan sequences

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