Page 113 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 113
COMPLEX ANALYSIS AND GEOMETRY (MS-17)
a sphere. The invariant can be computed easily and distinguishes many well-known equiva-
lent classes of CR maps between spheres. In particular, it vanishes precisely when the map is
spherical equivalent to the linear embedding. This is a joint work with Bernhard Lamel.
Equivalence of neighborhoods of embedded compact complex manifolds
and higher codimension foliations
Laurent Stolovitch, stolo@unice.fr
CNRS-Université Côte d’Azur, France
Coauthor: Xianghong Gong
We consider an embedded n-dimensional compact complex manifold in n+d dimensional com-
plex manifolds. We are interested in the holomorphic classification of neighborhoods as part of
Grauert’s formal principle program. We will give conditions ensuring that a neighborhood of
Cn in Mn+d is biholomorphic to a neighborhood of the zero section of its normal bundle. This
extends Arnold’s result about neighborhoods of a complex torus in a surface. We also prove the
existence of a holomorphic foliation in Mn+d having Cn as a compact leaf, extending Ueda’s
theory to the high codimension case. Both problems appear as a kind linearization problem
involving small divisors condition arising from solutions to their cohomological equations.
Weighted-L2 polynomial approximation in C
Jujie Wu, jujie.wu@ntnu.no
Norwegian University of Science and Technology, Norway, and Henan University, China
We study the density of polynomials in H2(Ω, e−ϕ), the space of square integrable holomorphic
functions in a bounded domain Ω in C, where ϕ is a subharmonic function. In particular, we
prove that the density holds in Carathéodory domains for any subharmonic function ϕ in a
neighborhood of Ω. In non-Carathéodory domains, we prove that the density depends on the
weight function, giving examples. This is joint with Séverine Biard and John Erik Fornæss.
A criterion of Nakano positivity
Xiangyu Zhou, xyzhou@math.ac.cn
Inst. of Mathematics, Chinese Academy of Sciences, China
How to characterize Nakano positivity of holomorphic vector bundles is a difficult problem
in complex geometry. In this talk, we’ll give a criterion of Nakano positivity in terms of L2
extensions. This is joint work with Fusheng Deng, Jiafu Ning, Zhiwei Wang.
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a sphere. The invariant can be computed easily and distinguishes many well-known equiva-
lent classes of CR maps between spheres. In particular, it vanishes precisely when the map is
spherical equivalent to the linear embedding. This is a joint work with Bernhard Lamel.
Equivalence of neighborhoods of embedded compact complex manifolds
and higher codimension foliations
Laurent Stolovitch, stolo@unice.fr
CNRS-Université Côte d’Azur, France
Coauthor: Xianghong Gong
We consider an embedded n-dimensional compact complex manifold in n+d dimensional com-
plex manifolds. We are interested in the holomorphic classification of neighborhoods as part of
Grauert’s formal principle program. We will give conditions ensuring that a neighborhood of
Cn in Mn+d is biholomorphic to a neighborhood of the zero section of its normal bundle. This
extends Arnold’s result about neighborhoods of a complex torus in a surface. We also prove the
existence of a holomorphic foliation in Mn+d having Cn as a compact leaf, extending Ueda’s
theory to the high codimension case. Both problems appear as a kind linearization problem
involving small divisors condition arising from solutions to their cohomological equations.
Weighted-L2 polynomial approximation in C
Jujie Wu, jujie.wu@ntnu.no
Norwegian University of Science and Technology, Norway, and Henan University, China
We study the density of polynomials in H2(Ω, e−ϕ), the space of square integrable holomorphic
functions in a bounded domain Ω in C, where ϕ is a subharmonic function. In particular, we
prove that the density holds in Carathéodory domains for any subharmonic function ϕ in a
neighborhood of Ω. In non-Carathéodory domains, we prove that the density depends on the
weight function, giving examples. This is joint with Séverine Biard and John Erik Fornæss.
A criterion of Nakano positivity
Xiangyu Zhou, xyzhou@math.ac.cn
Inst. of Mathematics, Chinese Academy of Sciences, China
How to characterize Nakano positivity of holomorphic vector bundles is a difficult problem
in complex geometry. In this talk, we’ll give a criterion of Nakano positivity in terms of L2
extensions. This is joint work with Fusheng Deng, Jiafu Ning, Zhiwei Wang.
111
