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Divisors on symmetric products of curves. (English) Zbl 0788.14019

Let \(C\) be a smooth irreducible curve of genus \(g\) and let \(C_ d\) be its \(d\)-fold symmetric product. For a curve \(C\) with general moduli its Néron-Severi group is generated by the classes of two divisors. If \(\vartheta\) and \(x\) stand for those classes, the slope of a divisor on \(C_ d\), whose class is \(a\vartheta-bx\), is defined by \(b/a\). The author looks for lower and upper bounds for the slope of effective and ample divisors on \(C_ d\).

MSC:

14H10 Families, moduli of curves (algebraic)
14C20 Divisors, linear systems, invertible sheaves
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References:

[1] E. Arbarello, M. Cornalba, P. Griffiths, and J. Harris, Geometry of algebraic curves. I, Springer, 1985. · Zbl 0559.14017
[2] Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. · Zbl 0367.14001
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