scholarly journals On the closedness of singular loci

1959 ◽  
Vol 2 (1) ◽  
pp. 5-12 ◽  
Author(s):  
Masayoshi Nagata
Keyword(s):  
2003 ◽  
Vol 355 (10) ◽  
pp. 3915-3945 ◽  
Author(s):  
Sara C. Billey ◽  
Gregory S. Warrington

1998 ◽  
Vol 09 (07) ◽  
pp. 921-921
Author(s):  
ADAM HARRIS

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.


1998 ◽  
Vol 09 (03) ◽  
pp. 277-293
Author(s):  
ADAM HARRIS

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.


2008 ◽  
Vol 319 (11) ◽  
pp. 4759-4779 ◽  
Author(s):  
J. Brown ◽  
V. Lakshmibai

2020 ◽  
Vol 17 (09) ◽  
pp. 2050141 ◽  
Author(s):  
Jianguo Sun

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.


2010 ◽  
Vol 59 (2) ◽  
pp. 243-267
Author(s):  
J. Brown ◽  
V. Lakshmibai

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

1997 ◽  
Vol 08 (05) ◽  
pp. 689-702 ◽  
Author(s):  
Shun Shimomura

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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