Year: 2026
Type: article
Abstract: Let be a complex analytic reduced curve singularity of arbitrary large embedded dimension. Its lattice cohomology ⁎ was introduced in [2] , each is a graded –module. Here we study its homological version ⁎ . The construction uses the multivariable Hilbert function associated with the valuations provided by the normalization of the curve. A key intermediate product is a tower of topological spaces such that . In this article for every n we consider a natural filtration of the space , which provides a homological spectral sequence converging to the homogeneous summand of the lattice homology. All the entries of all the pages of the spectral sequences are new invariants of . We show that the collection of the ranks of the entries of the first pages is equivalent with the motivic Poincaré series of . We provide several concrete computations of the corresponding multivariable Poincaré series associated with the entries of the spectral sequences. In the case of plane curve singularities, the first page can also be identified with the Heegaard Floer Link homology of the link of the singularity. In this way, the new invariants provide for an arbitrary (non necessarily plane) singularity a homological theory which is the analogue of the Heegaard Floer Link theory (formulated for links in the 3–sphere).
Source: Advances in Mathematics
Author: András Némethi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,790
OpenAlex ID: W7204192636