Abel maps and limit linear series for curves of compact type with three irreducible components
\textit{B. Osserman} [Ann. Inst. Fourier 56, No. 6, 1165--1205 (2006; Zbl 1118.14037)] refined and extended the classical theory of limit linear series due to \textit{D. Eisenbud} and \textit{J. Harris} [Invent. Math. 85, 337--371 (1986; Zbl 0598.14003)]. Let \({\mathfrak{g}}\) the unique exact extension of an \(r\)-dimensional refined Eisenbud-Harris limit linear series. Among the many applications Ossermann's theory there is a link to the Abel maps of reducible nodal curves [\textit{E. Esteves} and \textit{B. Osserman}, Rend. Circ. Mat. Palermo (2) 62, No. 1, 79--95 (2013; Zbl 1297.14035)] who introduced a closed subscheme \(\mathbb {P}(\mathfrak{g})\) of the Abel's map and made a detailed study for the case of curve with \(2\) irreducible components. In this paper the author does the case of curves with compact type and \(3\) components. He finds the irreducible components of \(\mathbb {P}(\mathfrak{g})\), proves that it is connected of pure dimension \(r\) and computes its Hilbert polynomial.
scientific article; zbMATH DE number 6971583