On unexpected curves of type (d+k,d)

2021/09/02 by Malara, Grzegorz, Tutaj-Gasińska, Halszka
#14C20 #14N20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.00769

Abstract

We present a construction explaining the existence of (unexpected) curves of degree d+k, passing through a set Z of points on ℙ², and having a generic point P of multiplicity d. The construction is based on the syzygies of the k-th powers of Jacobian of the product of lines dual to the points of Z. We prove also a result characterizing the unexpectedness of the curves via splitting type of the bundle of these syzygies retricted to the line dual to P.

Related

• Unexpected curves in ℙ², line arrangements, and minimal degree of Jacobian relations
• Unexpected hypersurfaces of type (d+k,d)
• Diminished Fermat-type arrangements and unexpected curves
• Unexpected hypersurfaces and where to find them
• Curves with Jacobian syzygies of the same degree