# Questions tagged [singular-support]

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Let $M$ be a real analytic manifold. Let $F$ be an object of the bounded derived category of sheaves on $M$ with real constructible cohomology sheaves. Let $CC(F)$ denote the characteristic cycle of $... 1 vote 0 answers 39 views ### Is the cone$\Sigma(T)$orthogonal to the singular support of a distribution? Hello I am totally new to microlocal analysis and I have a question. Is the cone$\Sigma(T)$orthogonal to the singular support of a distribution? $$\xi \notin \Sigma(T) \iff \exists V\ conic\ ... 1 vote 1 answer 117 views ### Stratification along which a constructible complex is smooth Let X be a smooth complex algebraic variety. A constructible complex F on X has a singular support SS(F)\subset T^*X. Assume you are given a stratification of X such that SS(F) is the ... 3 votes 0 answers 55 views ### Is the characteristic cycle map for perverse sheaves injective? Let X be a smooth irreducible complex variety. Is the characteristic cycle map from the Grothendieck group of perverse sheaves (with complex coefficients) on X to the free abelian group generated ... 3 votes 1 answer 78 views ### Singular Radon probabilities on [0,1]^d. Is conditioning on x_i = \alpha well-defined? The question: Let \pi be a Radon probability measure on [0,1]^d, 2\leq d < \omega, that is singular (w.r.t. to the d-dimensional Lebesgue measure). Suppose that for i\in \{1,\dots,d\} and ... 2 votes 0 answers 122 views ### Limit involving singular kernel: \lim_{s\to 1}(1-s)\int_{\Omega}\frac{(u(x)-u(y))}{|x-y|^{d+2s}} d y. Let \Omega\subset \Bbb R^d be a bounded C^1 domain. Let u:\Bbb R^d\to \Bbb R be a function in C^2_b(\Bbb R^d). I would like to compute the following limit: for x\in \partial \Omega$$L= \... 8 votes 0 answers 223 views ### Why mu-stratifications? In the microlocal theory of sheaves developed by Kashiwara and Schapira, there is the notion of a$\mu$-stratification, which is a stratification satisfying a stronger property ("$\mu$") than Whitney'... 3 votes 1 answer 275 views ### Wavefront set and Duhamel's principle Consider the Cauchy problem: $$\frac{\partial u}{\partial t} + \mathrm{i}\mkern1mu A(x,D_x) u = f \quad 0< t < T; \qquad u = u_0 \quad \text{when}\; t = 0,$$ where$A$has real principal ... 4 votes 1 answer 194 views ### Interesting (non) examples of singular support I'm trying to better understand singular support of sheaves on smooth manifolds---to this end: What are examples of conical subsets of$T^*X$that cannot arise as the singular support of a sheaf on$...
Let $\mathcal S'=\mathcal S'(\mathbb R^n)$ be the Schwartz distribution space. Suppose $A\colon\mathcal S'\to\mathcal S'$ is linear, continuous and microlocal. By being microlocal I mean that the wave ...
For constructible sheaves $\mathcal F$ on real analytic manifolds $X$, there is a notion of the singular support $SS(\mathcal F)$ which is a radially invariant singular Lagrangian subset of the ...