Multiple-point residue formulas for holomorphic maps

2021/12/31 by Bérczi, Gergely, Szenes, András · 1 citation
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.15502

Abstract

We develop a new approach to the study of the multipoint loci of holomorphic maps between complex manifolds. We relate the k-fold locus to the curvilinear component of the Hilbert scheme of k points on the source space of the map, and using equivariant localisation, we derive a closed iterated multipoint residue formula. Our work is motivated by ideas and conjectures of M. Kazarian and R. Rimányi on residual polynomials.

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• Higher characteristic classes of multisingularity loci

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