Patchworking singular algebraic curves I
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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.
KeywordsSingular Point Exact Sequence Line Bundle Algebraic Surface Singular Curve
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- R. Hartschorne,Algebraic Geometry, Springer-Verlag, Berlin, 1977.Google Scholar
- D. Hilbert,Mathematische Probleme, Archiv der Mathematik und Physik3 (1901), 213–237 (German).Google Scholar
- E. Shustin,Lower deformations of isolated hypersurface singularities, Algebra i Analiz10 (1999), 221–249 (English translation: St. Petersburg Mathematical Journal11 (2000), 883–908).Google Scholar
- E. Shustin and I. Tyomkin,Patchworking singular algebraic curves II, Israel Journal of Mathematics, this volume.Google Scholar
- O. Ya. Viro,Gluing of algebraic hypersurfaces, smoothing of singularities and construction of curves, Proceedings of the Leningrad International Topological Conference, Leningrad, Aug. 1982, Nauka, Leningrad, 1983, pp. 149–197 (Russian).Google Scholar
- O. Viro,Gluing of plane real algebraic curves and constructions of curves of degrees 6 and 7, Lecture Notes in Mathematics1060, Springer-Verlag, Berlin, 1984, pp. 187–200.Google Scholar
- O. Viro,Introduction to Topology of Real Algebraic Varieties, Preprint, appears in the internet at http://www.math.uu.se/~oleg/es/index.html.Google Scholar
- O. Viro,Patchworking real algebraic varieties, Preprint, appears in the internet at http://www.math.uu.se/~oleg/pw.ps.Google Scholar