scholarly journals On the closedness of singular loci

1959 ◽  
Vol 2 (1) ◽  
pp. 5-12 ◽  
Author(s):  
Masayoshi Nagata
Keyword(s):  
Singular Loci

scholarly journals Maximal singular loci of Schubert varieties in $SL(n)/B$

2003 ◽  
Vol 355 (10) ◽  
pp. 3915-3945 ◽  
Author(s):  
Sara C. Billey ◽  
Gregory S. Warrington
Keyword(s):  
Schubert Varieties ◽  
Singular Loci

REMARK ON THE ARTICLE "SINGULAR LOCI IN HOLOMORPHIC FAMILIES"

1998 ◽  
Vol 09 (07) ◽  
pp. 921-921
Author(s):  
ADAM HARRIS
Keyword(s):  
Essential Role ◽  
Open Neighbourhood ◽  
Complex Manifolds ◽  
Complex Spaces ◽  
Basic Assumptions ◽  
Singular Loci

To the basic assumptions that the map [Formula: see text] is a proper, flat morphism between complex manifolds should be added the hypothesis that the fibres of π are all generically reduced complex spaces. The existence of a non-empty open neighbourhood in [Formula: see text] plays an essential role in the proof of the main theorem, and does not follow automatically from the hypotheses as they were originally stated.

SINGULAR LOCI IN HOLOMORPHIC FAMILIES

1998 ◽  
Vol 09 (03) ◽  
pp. 277-293
Author(s):  
ADAM HARRIS
Keyword(s):  
Vector Bundles ◽  
A Priori ◽  
Complex Structure ◽  
Compact Complex Manifold ◽  
Entire Family ◽  
Analytic Subset ◽  
Degeneracy Loci ◽  
Singular Spaces ◽  
Singular Loci ◽  
Complex Projective

Let [Formula: see text] be a proper flat morphism between manifolds, and [Formula: see text] an analytic subset, such that the fibres Xt, for all [Formula: see text], determine a locally trivial deformation of a compact complex manifold. Non-generic fibres Xt, for t ∈ A, may be taken a priori to be singular spaces, or to have a smooth complex structure which is biholomorphically distinct from their generic neighbours. The main theorem of this article provides a sufficient condition for local triviality of the entire family [Formula: see text], in terms of the dimension of A and of the singular subvarieties of certain "degeneracy loci" in [Formula: see text]. Several specific applications of the main theorem are subsequently examined, some of which correspond sharply with examples of "structure-jumping" in complex deformations and "jumping loci" of vector bundles on complex projective space.

scholarly journals Singular loci of Bruhat–Hibi toric varieties

2008 ◽  
Vol 319 (11) ◽  
pp. 4759-4779 ◽  
Author(s):  
J. Brown ◽  
V. Lakshmibai
Keyword(s):  
Toric Varieties ◽  
Singular Loci

Singularity properties of null killing magnetic curves in Minkowski 3-space

2020 ◽  
Vol 17 (09) ◽  
pp. 2050141 ◽  
Author(s):  
Jianguo Sun
Keyword(s):  
Vector Field ◽  
Magnetic Vector ◽  
Geometrical Properties ◽  
Singular Loci ◽  
Magnetic Curve

We reconstruct the Cartan Equations of null Killing magnetic curve [Formula: see text] in [Formula: see text] with Killing magnetic vector field [Formula: see text] under the new Cartan frame [Formula: see text], which describe some new geometrical properties of [Formula: see text]. The singularity properties of the rectifying surfaces and the binormal osculating surfaces of null Killing magnetic curves are given. As an application, two examples are given to explain the main results, where the singular loci of null Killing magnetic curves are obtained.

scholarly journals Singular loci of Grassmann-Hibi toric varieties

2010 ◽  
Vol 59 (2) ◽  
pp. 243-267
Author(s):  
J. Brown ◽  
V. Lakshmibai
Keyword(s):  
Toric Varieties ◽  
Singular Loci

scholarly journals Singular Loci of Varieties of Complexes, II

2001 ◽  
Vol 235 (2) ◽  
pp. 547-558 ◽  
Author(s):  
Nicolae Gonciulea
Keyword(s):  
Singular Loci

A System Associated with the Confluent Hypergeometric Function Φ3 and a Certain Linear Ordinary Differential Equation with Two Irregular Singular Points

1997 ◽  
Vol 08 (05) ◽  
pp. 689-702 ◽  
Author(s):  
Shun Shimomura
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Hypergeometric Function ◽  
Confluent Hypergeometric Function ◽  
Linear Ordinary Differential Equation ◽  
Singular Points ◽  
Third Order ◽  
Regular Type ◽  
Singular Loci ◽  
Irregular Singular Points

The confluent hypergeometric function Φ3 satisfies a system of partial differential equations on P1(C) × P1(C) with the singular loci x = 0, x = ∞, y = ∞ of irregular type and y = 0 of regular type. We obtain asymptotic expansions and Stokes multipliers of linearly independent solutions near the singular loci x = 0 and x = ∞. Applying the results we also clarify the global behaviour of the solutions of a third order linear ordinary differential equation with two irregular singular points.

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