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Trigonal Gorenstein curves and special linear systems. (English) Zbl 0997.14007

Summary: Let \(Y\) be a Gorenstein trigonal curve with \(g:= p_a(Y)\geq 0\). Here we study the theory of special linear systems on \(Y\), extending the classical case of a smooth \(Y\) given by A. Maroni [Ann. Mat. Pura Appl., IV. Ser. 25, 343-354 (1946; Zbl 0061.35407)]. As in the classical case, to study it we use the minimal degree surface scroll containing the canonical model of \(Y\). The answer is different if the degree 3 pencil on \(Y\) is associated to a line bundle or not. We also give the easier case of special linear series on hyperelliptic curves. The unique hyperelliptic curve of genus \(g\) which is not Gorenstein has no special spanned line bundle.

MSC:

14H51 Special divisors on curves (gonality, Brill-Noether theory)
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14C20 Divisors, linear systems, invertible sheaves

Citations:

Zbl 0061.35407
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References:

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