Results 201 to 210 of about 27,767 (221)

Non‐archimedean stratifications of tangent cones

Mathematical Logic Quarterly, 2017
AbstractWe study the impact of a kind of non‐archimedean stratifications (t‐stratifications) on tangent cones of definable sets in real closed fields. We prove that such stratifications induce stratifications of the same nature on the tangent cone of a definable set at a fixed point.
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Intersection multiplicities and tangent cones

Mathematical Proceedings of the Cambridge Philosophical Society, 1979
The following result has at least the appeal of intuitive plausibility. Let U and V be subvarieties of an algebraic variety X; let x ∈ X be an isolated point of the intersection of U and V, and let I(X, U. V, x) denote the intersection multiplicity (in some sense to be made precise) of U and V at x.
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On semialgebraic tangent cones

1998
Summary: The paper deals with the following question: Which semialgebraic subsets of \(\mathbb{R}^n\) can be realized as tangent cones to real algebraic subsets of \(\mathbb{R}^n\)? At first we prove that the answer is positive for every closed semialgebraic cone in \(\mathbb{R}^n\) of dimension \(\leq 2\). Then, for closed semialgebraic cones \(A\) in
FERRAROTTI M, FORTUNA, ELISABETTA
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Tangent cones and Dini derivatives

Journal of Optimization Theory and Applications, 1991
Characterizations of the Bouligand contingent cone to the epigraph and graph of a locally Lipschitz function are given. It is proved that, if f:H\(\mapsto {\mathbb{R}}\) is a locally Lipschitz function on a Hilbert space H, then \(T_{Epi(f)}(x,f(x))=\{(x',y')| \quad \exists \{a_ n\}^{\infty}_{n=1},\quad \{y_ n\}^{\infty}_{n=1}\subset {\mathbb{R}},\quad
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Singular Points and Tangent Cones

1992
The Zariski tangent space to a variety X ⊂ 𝔸n at a point p is described by taking the linear part of the expansion around p of all the functions on 𝔸n vanishing on X. In case p is a singular point of X, however, this does not give us a very refined picture of the local geometry of X; for example, if X ⊂ 𝔸2 is a plane curve, the Zariski tangent space to
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STABLE MINIMAL HYPERSURFACES AND TANGENT CONE SINGULARITIES

International Journal of Mathematics, 1999
In this paper, I give an estimate on the dimension of the singular set of a tangent cone at infinity of a stable minimal hypersurface. Namely, let Mn ⊂ ℝn+1, n ≥ 2, be a complete orientable stable minimal immersion with bounded volume growth. Then n < 7 implies T∞(M) is smooth, and n ≥ 7 implies the singular set of T∞(M) has codimension at least ...
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Tangent Cones and Intersection Theory

1989
Let E be an arbitrary set in ℝ N . A vector ν ∈ ℝ N is called tangent to E at a point a ∈ Ē if there exist a sequence of points a j ∈ E and numbers t j > 0 such that a j → a and t j (a j − a) → ν as j→ ∞. The set of all such tangent vectors is denoted by C(E, a) and is called the tangent cone to E at a.
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Tangent Cones

2008
Jean-Pierre Aubin, Hèléne Frankowska
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Tangent cones and analytic branches

1986
Let X be an algebraic variety over an algebraically closed field. Let Y be an irreducible subvariety of X of codimension 1 with generic point y. The structure of the tangent cone \(T_{X,x}\) of X at almost all closed points x in Y is compared to that of \(T_{x,y}\). This is done by using the theory of branches as developed by \textit{S. Greco} in Proc.
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Tangent Cones, Tangent Spaces, Tangent Stars: Secant, Tangent, Tangent Star and Dual Varieties of an Algebraic Variety

2016
We recall the definitions of tangent cone, tangent space, tangent star to a variety at a fixed point, define the secant variety SX, the higher secant varieties S k X, the tangent variety TX and the variety of tangent stars T∗X of a variety \(X \subset \mathbb{P}^{N}\). We consider the join of a variety \(X \subset \mathbb{P}^{N}\) with another variety \
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