On Weierstrass nodes (Q2077165)

The main result of this paper describes when a node of a stable curve is the limit of Weierstrass points from nearby smooth curves. Moreover, the author genearlizes the result to \(k\)-Weierstrass points with respect to the \(k\)-canonical linear systems. The author also classifies the \(k\)-Weierstrass gap sequences in genus two. The proofs of these results rely on the boundary description of the strata of differentials in [\textit{M. Bainbridge} et al., Duke Math. J. 167, No. 12, 2347--2416 (2018; Zbl 1403.14058); Algebr. Geom. 6, No. 2, 196--233 (2019; Zbl 1440.14148)].