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Patchworking singular algebraic curves. I. (English) Zbl 1128.14019
This paper is devoted to the presentation of a general patchworking procedure to construct reduced singular complex curves having prescribed singularities and belonging to a given linear system on an algebraic surface. The patchworking procedure to construct a curve $$C$$ with singularities of given type on an algebraic surface $$X$$ uses a reducible surface $$X_0$$ which is a degeneration of $$X$$, then construct a curve $$C_0$$ on $$X_0$$ and prove that $$C_0$$ deforms to $$C$$ on $$X$$.
The paper under review significantly generalizes the preceding works by the authors and others by using weaker assumptions to prove that $$C_0$$ deforms to $$C$$ on $$X$$. In the second part of this paper [Isr. J. Math. 151, 145–166 (2006; Zbl 1128.14020)], the authors apply this general procedure to produce detailed examples.

##### MSC:
 14H20 Singularities of curves, local rings
##### Keywords:
Viro method; singular curves
Full Text:
##### References:
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