A question of divisibility of an analytic germ by a polynomial

2000 ◽  
Vol 1 (2) ◽  
pp. 157-162
Author(s):  
Zofia Denkowska
Keyword(s):  
Analytic Germ

scholarly journals Singularity of the varieties of representations of lattices in solvable Lie groups

2016 ◽  
Vol 08 (02) ◽  
pp. 273-285 ◽  
Author(s):  
Hisashi Kasuya
Keyword(s):  
Lie Group ◽  
Vector Bundles ◽  
Similar Technique ◽  
Trivial Representation ◽  
Nilpotent Lie Algebra ◽  
Solvable Lie Groups ◽  
Analytic Germ ◽  
Space Construction ◽  
Simply Connected ◽  
Solvable Lie Group

For a lattice [Formula: see text] of a simply connected solvable Lie group [Formula: see text], we describe the analytic germ in the variety of representations of [Formula: see text] at the trivial representation as an analytic germ which is linearly embedded in the analytic germ associated with the nilpotent Lie algebra determined by [Formula: see text]. By this description, under certain assumption, we study the singularity of the analytic germ in the variety of representations of [Formula: see text] at the trivial representation by using the Kuranishi space construction. By a similar technique, we also study deformations of holomorphic structures of trivial vector bundles over complex parallelizable solvmanifolds.

scholarly journals Tauberian theorems for k–summability with respect to an analytic germ

2020 ◽  
Vol 489 (2) ◽  
pp. 124174
Author(s):  
Sergio A. Carrillo ◽  
Jorge Mozo-Fernández ◽  
Reinhard Schäfke
Keyword(s):  
Tauberian Theorems ◽  
Analytic Germ

scholarly journals Local systems on analytic germ complements

2017 ◽  
Vol 306 ◽  
pp. 905-928 ◽  
Author(s):  
Nero Budur ◽  
Botong Wang
Keyword(s):  
Local Systems ◽  
Analytic Germ

scholarly journals Asymptotic expansions and summability with respect to an analytic germ

2019 ◽  
Vol 63 ◽  
pp. 3-79 ◽  
Author(s):  
Jorge Mozo Fernández ◽  
Reinhard Schäfke
Keyword(s):  
Asymptotic Expansions ◽  
Analytic Germ

REAL ANALYTIC GERMS $f \bar{g}$ AND OPEN-BOOK DECOMPOSITIONS OF THE 3-SPHERE

2005 ◽  
Vol 16 (01) ◽  
pp. 1-12 ◽  
Author(s):  
ANNE PICHON
Keyword(s):  
Large Family ◽  
Open Book ◽  
Tubular Neighbourhood ◽  
Isolated Singularity ◽  
Isolated Singularities ◽  
The Real ◽  
Milnor Fibration ◽  
Analytic Germ ◽  
Open Book Decompositions ◽  
Real Analytic

Let f,g: (C2,0) → (C,0) be two holomorphic germs with isolated singularities and no common branches and let Lf, [Formula: see text] be their links. We prove that the real analytic germ [Formula: see text] has an isolated singularity at 0 if and only if the link Lf ∪ -Lg is fibred. This was conjectured by Rudolph in [14]. If this condition holds, then the underlying Milnor fibration is an open-book fibration of the link Lf ∪ -Lg which coincides with [Formula: see text] in a tubular neighbourhood of this link. This enables one to realize a large family of fibrations of plumbing links in S3 as the Milnor fibrations of some real analytic germs [Formula: see text].

On the extension theorem of Hwang and Mok

2018 ◽  
Vol 2018 (743) ◽  
pp. 1-27
Author(s):  
Jan Gutt
Keyword(s):  
Geometric Structure ◽  
Extension Theorem ◽  
General Point ◽  
Picard Number ◽  
Fano Manifold ◽  
Analytic Germ ◽  
Fubini Extension

Abstract Jun-Muk Hwang and Ngaiming Mok developed a framework for studying complex Fano (more generally, uniruled) manifolds in terms of their intrinsic local differential-geometric structure: the varieties of minimal rational tangents (VMRT). In particular, their ‘Cartan–Fubini’ extension theorem shows that a Fano manifold of Picard number 1 (satisfying certain technical conditions) is determined, up to biholomorphism, by an analytic germ of its VMRT at a general point. We prove a characteristic-free analogue of this result, replacing the VMRT with families of formal arcs.

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