2024/06/25 by Caporaso, Lucia, Turchet, Amos · 1 citation
#14H20 #14H50 #14T90 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2406.17392
We study integral plane curves meeting at a single unibranch point and show that such curves must satisfy two equivalent conditions. A numeric condition: the local invariants of the curves at the contact point must be arithmetically related. A geometric condition: the tropical curves that we associate to the contact point must be isomorphic. Moreover, we prove closed formulas for the delta-invariant of a unibranch singularity, and for the dimension of the loci of curves with an assigned unibranch point. Our work is motivated by interest in the Lang exceptional set.