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Limit linear series: Basic theory. (English) Zbl 0598.14003
In this important paper the authors study the relation of linear series on a stable curve C with $$Pic^ 0(C)$$ compact and the linear series on nearby smooth curves. In papers which will appear soon, they apply their theory to many important topics (Kodaira dimension of $$M_ g$$, existence and monodromy of Weierstrass points). For another application, see the reviewer, Proc. Am. Math. Soc. 97, 217-218 (1986; Zbl 0591.14020).
Reviewer: E.Ballico

##### MSC:
 14C20 Divisors, linear systems, invertible sheaves 14H10 Families, moduli of curves (algebraic) 14H15 Families, moduli of curves (analytic) 14D15 Formal methods and deformations in algebraic geometry 14H45 Special algebraic curves and curves of low genus 14H55 Riemann surfaces; Weierstrass points; gap sequences
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##### References:
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