Patchworking singular algebraic curves I

Eugenii Shustin; Ilya Tyomkin

doi:10.1007/BF02777358

Patchworking singular algebraic curves I

Eugenii Shustin, Ilya Tyomkin

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English
Pages (from-to)	125-144
Number of pages	20
Journal	Israel Journal of Mathematics
Volume	151
DOIs	https://doi.org/10.1007/BF02777358
State	Published - 15 May 2006
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/BF02777358

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@article{77296d52baef4fd99dc7211a1fc01c74,

title = "Patchworking singular algebraic curves I",

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.",

author = "Eugenii Shustin and Ilya Tyomkin",

note = "Funding Information: * Both authors were partially supported by the Herman Minkowsky-Minerva Center for Geometry at Tel Aviv University, and by grant no. G-616-15.6/99 from the German-Israeli Foundation for Research and Development. The first author was also supported by the Bessel Research Award from the Alexander von Humboldt Foundation. The second author was also partially supported by the EC-network 'Algebraic Lie Representations' contract no. ERB-FMRX-CT97-0100. Received March 11, 2003 and in revised form November 19, 2003",

year = "2006",

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doi = "10.1007/BF02777358",

language = "English",

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journal = "Israel Journal of Mathematics",

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T1 - Patchworking singular algebraic curves I

AU - Shustin, Eugenii

AU - Tyomkin, Ilya

N1 - Funding Information: * Both authors were partially supported by the Herman Minkowsky-Minerva Center for Geometry at Tel Aviv University, and by grant no. G-616-15.6/99 from the German-Israeli Foundation for Research and Development. The first author was also supported by the Bessel Research Award from the Alexander von Humboldt Foundation. The second author was also partially supported by the EC-network 'Algebraic Lie Representations' contract no. ERB-FMRX-CT97-0100. Received March 11, 2003 and in revised form November 19, 2003

PY - 2006/5/15

Y1 - 2006/5/15

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/33646431978

U2 - 10.1007/BF02777358

DO - 10.1007/BF02777358

M3 - Article

AN - SCOPUS:33646431978

SN - 0021-2172

VL - 151

SP - 125

EP - 144

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Patchworking singular algebraic curves I

Abstract

ASJC Scopus subject areas

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