The intersection form of a plane isolated line singularity

1991 ◽  
pp. 172-184 ◽  
Author(s):  
V. V. Goryunov
Keyword(s):  
Intersection Form ◽  
Line Singularity

scholarly journals Non Kählerian surfaces with a cycle of rational curves

2021 ◽  
Vol 8 (1) ◽  
pp. 208-222
Author(s):  
Georges Dloussky
Keyword(s):  
Deformation Theory ◽  
Complex Surface ◽  
Rational Curves ◽  
Intersection Form ◽  
Connected Component ◽  
Hirzebruch Surface ◽  
Compact Complex Surface ◽  
A Chain

Abstract 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.

Characterizations of Simple Isolated Line Singularities

1999 ◽  
Vol 42 (4) ◽  
pp. 499-506 ◽  
Author(s):  
Alexandru Zaharia
Keyword(s):  
Function Germ ◽  
Critical Set ◽  
Line Singularity ◽  
Line Singularities

AbstractA line singularity is a function germ with a smooth 1-dimensional critical set . An isolated line singularity is defined by the condition that for every x ≠ 0, the germ of f at (x, 0) is equivalent to . Simple isolated line singularities were classified by Dirk Siersma and are analogous of the famous A − D − E singularities. We give two new characterizations of simple isolated line singularities.

Equivariant Intersection Theory and Surgery Theory for Manifolds with Middle Dimensional Singular Sets

2008 ◽  
Vol 2 (3) ◽  
pp. 507-600 ◽  
Author(s):  
Anthony Bak ◽  
Masaharu Morimoto
Keyword(s):  
Intersection Theory ◽  
Finite Family ◽  
Dimensional Sphere ◽  
Singular Set ◽  
Intersection Form ◽  
Surgery Theory ◽  
Equivariant Surgery ◽  
A Finite Group ◽  
Necessary And Sufficient ◽  
Simply Connected

AbstractLet G denote a finite group and n = 2k 6 an even integer. Let X denote a simply connected, compact, oriented, smooth G-manifold of dimension n. Let L denote a union of connected, compact, neat submanifolds in X of dimension k. We invoke the hypothesis that L is a G-subcomplex of a G-equivariant smooth triangulation of X and contains the singular set of the action of G on X. If the dimension of the G-singular set is also k then the ordinary equivariant self-intersection form is not well defined, although the equivariant intersection form is well defined. The first goal of the paper is to eliminate the deficiency above by constructing a new, well defined, equivariant, self-intersection form, called the generalized (or doubly parametrized) equivariant self-intersection form. Its value at a given element agrees with that of the ordinary equivariant self-intersection form when the latter value is well defined. Let denote a finite family of immersions withtrivial normal bundle of k-dimensional, connected, closed, orientable, smooth manifolds into X. Assume that the integral (and mod 2) intersection forms applied to members of and to orientable (and nonorientable) k-dimensional members of L are trivial. Then the vanishing of the equivariant intersection form on × and the generalized equivariant self-intersection form on is a necessary and sufficient condition that is regularly homotopic to a family of disjoint embeddings, each of which is disjoint from L. This property, when is a finite family of immersions of the k-dimensional sphere Sk into X, is just what is needed for constructing an equivariant surgery theory for G-manifolds X as above whose G-singular set has dimension less than or equal to k. What is new for surgery theory is that the equivariant surgery obstruction is defined for an almost arbitrary singular set of dimension k and in particular, the k-dimensional components of the singular set can be nonorientable.

scholarly journals On the Moving Contact Line Singularity

2019 ◽  
Vol 64 (1) ◽  
pp. 27-29
Author(s):  
R. V. Krechetnikov
Keyword(s):  
Contact Line ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Line Singularity

scholarly journals TRAPPING PHOTONS BY A LINE SINGULARITY

2003 ◽  
Vol 12 (06) ◽  
pp. 1095-1112 ◽  
Author(s):  
METIN ARIK ◽  
OZGUR DELICE
Keyword(s):  
Energy Density ◽  
Thin Shell ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Static Solutions ◽  
Line Singularity ◽  
Thick Shells

We present cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells. Positivity of the energy density of the thin shell and the line singularity is discussed. It is also shown that thick shells containing mostly radiation are possible in a numerical solution.

scholarly journals On the signatures of even 4-manifolds

2002 ◽  
Vol 132 (3) ◽  
pp. 453-469 ◽  
Author(s):  
CHRISTIAN BOHR
Keyword(s):  
Fundamental Group ◽  
Betti Numbers ◽  
Intersection Form ◽  
Group Invariant

In this paper we prove a number of inequalities between the signature and the Betti numbers of a 4-manifold with even intersection form and prescribed fundamental group. Furthermore, we introduce a new geometric group invariant and discuss some of its properties.

scholarly journals Shock-less Hypersonic Intakes

2021 ◽  
Author(s):  
Seyed Hossein Miri
Keyword(s):  
Exact Solution ◽  
Mach Number ◽  
Finite Volume Method ◽  
Conical Flow ◽  
Low Mach Number ◽  
Simulation Based ◽  
Line Singularity ◽  
Air Intake ◽  
Volume Method ◽  
Intake Flow

The accuracy of CFD for simulating hypersonic air intake flow is verified by calculating the flow inside a Busemann type intake. The CFD results are then compared against the “exact” solution for the Busemann intake as calculated from the Taylor-McColl equations for conical flow. The method proposed by G. Emanuel (the Lens Analogy) for generating an intake shape that transforms parallel and uniform hypersonic (freestream) flow isentropically to another parallel and uniform, less hypersonic, flow has been verified by CFD (SOLVER II) simulation, based on Finite Volume Method (FVM). The shock-less (isentropic) nature of the Lens Analogy (LA) flow shapes has been explored at both on and off-design Mach numbers. The Lens Analogy (LA) method exhibits a limit line (singularity) for low Mach number flows, where the streamlines perform an unrealistic reversal in direction. CFD calculations show no corresponding anomalies.

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