Semigroups, d-invariants and deformations of cuspidal singular points of plane curves

Abstract

We apply Heegaard Floer homology to study deformations of singularities of plane algebraic curves. Our main result provides an obstruction to the existence of a deformation between two singularities. Generalizations include the case of multiple singularities. The obstruction is formulated in terms of a semicontinuity property for semigroups associated to the singularities.

v2. 20 pages. Minor revision. Added comparison of the semigroup semicontinuity with a criterion obtained from the upsilon function of Ozsvath, Szabo and Stipsicz

References in corpus (3)

• Heegaard Floer homology and rational cuspidal curves
• Deformations of singularities of plane curves. Topological approach
• Bipartite graphs and combinatorial adjacency

Cited by in corpus (5)

• A note on cobordisms of algebraic knots
• Immersed concordances of links and Heegaard Floer homology
• Immersed disks, slicing numbers and concordance unknotting numbers
• Genus one cobordisms between torus knots
• On the First Singularity for the Upsilon Invariant of Algebraic Knots