Non Kählerian surfaces with a cycle of rational curves

Let S be a compact complex surface in class VII0+ containing a cycle of rational curves C = ∑Dj. Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C′ then C′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If ther...

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Autor principal:	Dloussky Georges
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	class vii kodaira classification compact non-kähler surface 32j15 32j27 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/9496f2987df6411baa6ba85ec1e8b294
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id	oai:doaj.org-article:9496f2987df6411baa6ba85ec1e8b294
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spelling	oai:doaj.org-article:9496f2987df6411baa6ba85ec1e8b2942021-12-05T14:10:45ZNon Kählerian surfaces with a cycle of rational curves2300-744310.1515/coma-2020-0114https://doaj.org/article/9496f2987df6411baa6ba85ec1e8b2942021-01-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0114https://doaj.org/toc/2300-7443Let S be a compact complex surface in class VII0+ containing a cycle of rational curves C = ∑Dj. Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C′ then C′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj. In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.Dloussky GeorgesDe Gruyterarticleclass viikodaira classificationcompact non-kähler surface32j1532j27MathematicsQA1-939ENComplex Manifolds, Vol 8, Iss 1, Pp 208-222 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	class vii kodaira classification compact non-kähler surface 32j15 32j27 Mathematics QA1-939
spellingShingle	class vii kodaira classification compact non-kähler surface 32j15 32j27 Mathematics QA1-939 Dloussky Georges Non Kählerian surfaces with a cycle of rational curves
description	Let S be a compact complex surface in class VII0+ containing a cycle of rational curves C = ∑Dj. Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C′ then C′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj. In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.
format	article
author	Dloussky Georges
author_facet	Dloussky Georges
author_sort	Dloussky Georges
title	Non Kählerian surfaces with a cycle of rational curves
title_short	Non Kählerian surfaces with a cycle of rational curves
title_full	Non Kählerian surfaces with a cycle of rational curves
title_fullStr	Non Kählerian surfaces with a cycle of rational curves
title_full_unstemmed	Non Kählerian surfaces with a cycle of rational curves
title_sort	non kählerian surfaces with a cycle of rational curves
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/9496f2987df6411baa6ba85ec1e8b294
work_keys_str_mv	AT dlousskygeorges nonkahleriansurfaceswithacycleofrationalcurves
_version_	1718371767027761152

Non Kählerian surfaces with a cycle of rational curves

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