Combinatorial patchworking of real pseudo-holomorphic curves

Ilia Itenberg; Eugenii Shustin

Makale detayları

Combinatorial patchworking of real pseudo-holomorphic curves

Yazarlar:

Ilia Itenberg | Eugenii Shustin

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2002 Vol.26 Issue 1, pp.27-52

Belge Tipi:

Makale

Yayın Tarihi:

12/2001

Belge Dili:

Türkçe

Document ID (Org No.):

2000749000

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

The Viro method of construction of real algebraic varieties  with prescribed topology uses convex subdivisions of Newton polyhedra.   We show that in the case of arbitrary (not necessarily convex)  subdivisions of polygons corresponding to C P2 and rational ruled  surfaces Sa, a \geq 0 the Viro method produces   pseudo-holomorphic curves.  The version of the Viro method discussed  in the paper also gives a possibility to construct singular  pseudo-holomorphic curves by gluing singular algebraic curves whose  collections of singularities do not permit to glue these curves in the  framework of the standard Viro method.  As an application, we  construct a series of singular real pseudo-holomorphic curves in C  P2 whose collections of singular points do not occur on known  algebraic curves of the same degree.

 

The Viro method of construction of real algebraic varieties  with prescribed topology uses convex subdivisions of Newton polyhedra.   We show that in the case of arbitrary (not necessarily convex)  subdivisions of polygons corresponding to C P2 and rational ruled  surfaces Sa, a \geq 0 the Viro method produces   pseudo-holomorphic curves.  The version of the Viro method discussed  in the paper also gives a possibility to construct singular  pseudo-holomorphic curves by gluing singular algebraic curves whose  collections of singularities do not permit to glue these curves in the  framework of the standard Viro method.  As an application, we  construct a series of singular real pseudo-holomorphic curves in C  P2 whose collections of singular points do not occur on known  algebraic curves of the same degree.

Makale detayları

Combinatorial patchworking of real pseudo-holomorphic curves

Yazarlar:

Ilia Itenberg | Eugenii Shustin

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2002 Vol.26 Issue 1, pp.27-52

Belge Tipi:

Makale

Yayın Tarihi:

12/2001

Belge Dili:

Türkçe

Document ID (Org No.):

2000749000

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Turk. J. Math.

26

(2002)

27-52. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.26

iss.1.

Sayı

Makale detayları

Combinatorial patchworking of real pseudo-holomorphic curves

Yazarlar: Ilia Itenberg | Eugenii Shustin

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2002 Vol.26 Issue 1, pp.27-52

Belge Tipi: Makale

Yayın Tarihi: 12/2001

Belge Dili: Türkçe

Document ID (Org No.): 2000749000

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Turk. J. Math.

26

(2002)

27-52. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.26

iss.1.

Sayı

Yazarlar:

Ilia Itenberg | Eugenii Shustin

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2002 Vol.26 Issue 1, pp.27-52

Belge Tipi:

Makale

Yayın Tarihi:

12/2001

Belge Dili:

Türkçe

Document ID (Org No.):

2000749000

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098