Structural properties of the lattice cohomology of curve singularities

• Alexander A. Kubasch ^[1] ; András Némethi ^[1] ; Gergő Schefler ^[1]
  1. [1] Alfréd Rényi Institute of Math., Budapest, Hungary
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01073-2
• Enlaces
  • Texto completo
• Resumen

  • The lattice cohomology of a reduced curve singularity was introduced in [4]. It is a bigraded ℤ[U]-module ?* = ⊕_{q,n} ?^{q}_{2n}, that categorifies the δ-invariant and extracts key geometric information from the semigroup of values.

    In the present paper we prove three structure theorems for this new invariant: (a) the weight-grading of the reduced cohomology is – just as in the case of the topological lattice cohomology of normal surface singularities [22] – nonpositive; (b) the graded ℤ[U]-module structure of ?⁰ determines whether or not a given curve is Gorenstein; and finally (c) the lattice cohomology module ?⁰ of any plane curve singularity determines its multiplicity.

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