Abel maps and limit linear series for curves of compact type with three irreducible components
type: Item
instance of: scholarly article
title: Abel maps and limit linear series for curves of compact type with three irreducible components
zbMATH Open document ID: 1402.14040
author: Gabriel Muñoz
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2018-11-02T00:00:00Z
review text: \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.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14H50
zbMATH DE Number: 6971583
zbMATH Keywords: nodal curves
zbMATH Keywords: stable curves
zbMATH Keywords: limit linear series
zbMATH Keywords: Abel maps
MaRDI profile type: Publication
full work available at URL: s00574-018-0071-2
OpenAlex ID: W2783282150
cites work: Abel maps for curves of compact type
cites work: Limit linear series: Basic theory
cites work: Abel maps and limit linear series
cites work: A limit linear series moduli scheme
cites work: Linked Grassmannians and crude limit linear series
DOI: 10.1007/S00574-018-0071-2
description: scientific article; zbMATH DE number 6971583