Pacienza, Gianluca On the nef cone of symmetric products of a generic curve. (English) Zbl 1056.14042 Am. J. Math. 125, No. 5, 1117-1135 (2003). Let \(C\) be a general curve of genus \(g \geq 1\). For any integer \(k>0\), let \(C^{(k)}\) denote its \(k\)-th symmetric product. Let \(N^1(C^{(k)})\) be the Neron-Severi group of \(C^{(k)}\) and \(\text{Nef}(C^{(k)}) \subset N^1(C^{(k)})\) the convex cone of the nef divisors. First, the author shows how to determine \(\text{Nef}(C^{(k)})\) when \(k\) is at least the gonality of \(C\), i.e. \(g \geq \lfloor g/2\rfloor +1\). The main result is its computation in the next case: \(g\) even and \(k = g/2\). Reviewer: Edoardo Ballico (Povo) Cited in 7 Documents MSC: 14H51 Special divisors on curves (gonality, Brill-Noether theory) 14C15 (Equivariant) Chow groups and rings; motives 14H99 Curves in algebraic geometry 14C20 Divisors, linear systems, invertible sheaves Keywords:nef class; curve with general moduli; Neron-Severi group PDFBibTeX XMLCite \textit{G. Pacienza}, Am. J. Math. 125, No. 5, 1117--1135 (2003; Zbl 1056.14042) Full Text: DOI