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Non-primitive linear systems on smooth algebraic curves and a generalization of Maroni theory. (English) Zbl 1172.14311

Summary: Let \(X\) be a smooth curve of genus \(g\) and \(M, L\) special spanned line bundles with \(h^0(X, L) = 2\) and \(h^0(X, M \otimes L^*) = h^0(X, M) - 2 > 0\). Generalizing Maroni theory for trigonal curves we study the existence of such triples \((X, M, L)\) for certain numerical invariants and classify all spanned line bundles, \(R\), on any such \(X\) with \(h^0(X, M\otimes R^*) > 0\). We construct smooth curves with non-primitive special linear systems with prescribed numerical invariants.

MSC:

14H10 Families, moduli of curves (algebraic)
14H51 Special divisors on curves (gonality, Brill-Noether theory)
14C20 Divisors, linear systems, invertible sheaves
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