Involutive Heegaard Floer homology and rational cuspidal curves
Maciej Borodzik, Jennifer Hom
TL;DR
This paper applies involutive Heegaard Floer invariants to study the singular point configurations of rational cuspidal curves, revealing constraints for odd degrees but not for even degrees.
Contribution
It introduces new constraints on rational cuspidal curves of odd degree using involutive Heegaard Floer invariants, highlighting differences between odd and even degrees.
Findings
Constraints on singular configurations for odd degree curves
No similar constraints found for even degree curves
Application of involutive Heegaard Floer invariants to algebraic geometry
Abstract
We use invariants of Hendricks and Manolescu coming from involutive Heegaard Floer theory to find constraints on possible configurations of singular points of a rational cuspidal curve of odd degree in the projective plane. We show that the results do not carry over to rational cuspidal curves of even degree.
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