# Patchworking singular algebraic curves I

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## Abstract

In this paper we present a general patchworking procedure for the construction of reduced singular curves having prescribed singularities and belonging to a given linear system on algebraic surfaces. It originates in the Viro “gluing” method for the construction of real non-singular algebraic hypersurfaces. The general procedure includes almost all known particular modifications, and goes far beyond. Some applications and examples illustrate the construction.

## Keywords

Singular Point Exact Sequence Line Bundle Algebraic Surface Singular Curve
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© The Hebrew University Magnes Press 2006