# All Questions

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### What is “graph-directed iterated function”?

Im translating an article about Rauzy fractal and I ran into this sentence: ...
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### Mirror symmetry for polarized abelian surfaces and Shioda-Inose K3s

It is well known (cf. Dolgachev) that there is a beautiful notion of mirror symmetry for lattice-polarized K3 surfaces. That is, if we are given a rank $r$ lattice $M$ of signature $(1, r - 1)$ and a ...
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### First passage time of a pure drift process

I am facing the following unusual problem: $Z_t$ is a pure drift process of the form $$dZ_t = \kappa(X_t - Z_t) dt$$ where $X_t$ is another bounded process. I am interested in computing / ...
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### Push-forward of locally free sheaves

Let $X, Y$ be smooth projective varieties and $f:X \times Y \to Y$ be the natural projetion map. Let $\mathcal{F}$ be a locally free sheaf on $X \times Y$. Is it true that $f_*\mathcal{F}$ is locally ...
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### dual composition of binary relations

I'm not sure if this is of any interest at all, but I spent some time looking at it a couple of years ago so I'd like to ask for input on this. Given two binary relations $\rho,\,\sigma$ on a set ...
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### Universal maps between topological spaces

Let $X,Y$ be topological spaces. We call a continuous map $u:X\to Y$ universal if for every continous map $f:X\to Y$ there is $x\in X$ such that $f(x) = u(x)$. If $u:X\to Y$ and $v:Y\to Z$ are ...
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### Rational conjugation of elements of a finite group

Let $G$ be a finite group. Two elements $x$ and $y$ of $G$ are said to be rationally conjugate, written $x \sim_{r} y$, if and only if $\langle x\rangle$ and $\langle y\rangle$ are conjugate subgroups ...
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### When can one find holomorphic sections vanishing at a point to a certain order?

Let $X$ be a compact complex manifold (say of dimension $2$) and $L \rightarrow X$ a holomorphic line bundle. Consider the following statements: Statement $A_0$: Given any point $p\in X$, there ...
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### Smoothness and smoothness over formal neighborhood

Let $f:X\rightarrow Y$ a locally finitely presented map. Let $x\in X$ and $y=f(x)$. We assume that the map on the level of fomal neighborhoods $X_{x}\rightarrow Y_{y}$ is formally smooth, can we find ...
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### Complex conjugate orbifold of C^n [on hold]

I have a very simple question: what is the result of identifying each point $(z_1,\ldots,z_n) \in \mathbb{C}^n$ with $(z_1^\ast,\ldots,z_n^\ast)$? Is it just $\mathbb{C}^{n-1} \times \mathbb{H}$, ...
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### Prove that the subset sum problem with fixed size and number reusability is NP complete

I'm trying to solve the following problem: There are B lists of unspecified size containing integers. Pick a number from each list so that the sum of all the picks is exactly A. Prove that this ...
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### Necessary conditions for optimality in Banach spaces

Let $X$ denote the non-negative "orthant" of the Banach space $L^2$ (or whatever you call the set of functions in $L^2$ that are non-negative), and let $C$ be a closed, convex subset of $X$. Let $f$ ...
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### Alternate proof of Schur orthogonality relations [migrated]

I am trying to find an alternate proof for Schur orthogonality relations along the following lines. Let $G$ be a finite group, with irreducible representations $V_1$, $V_2$, $\cdots$, $V_d$. Let $V$ ...
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### Help me with this Quadratic Equations [closed]

If x is and integer, which of the following must be an even integer. (1) x2-x-1 (2) x2-4x+6 (3) x2-5x+5 (4) x2+3x+8 (5) x2+2x+10 Please note that x2 means X square.
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### Picard of the product of two curves

Can anyone point to me where I can find the proof that the Picard group of the product of two curves is isomorphic to the product of the Picard groups times the hom among the Jacobians? Does the ...
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### Pyramid and intersections [closed]

Let P be a square pyramid whose base consists of the four vertices (0,0,0),(3,0,0),(3,3,0), and (0,3,0), and whose apex is the point (1,1,3). Let Q be a square pyramid whose base is the same as the ...