All Questions

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Example of symplectic 4-manifolds with no Lefschetz fibration structure?

I just read about Donaldson's result on existence of Lefschetz pencil structure on symplectic manifolds (Donaldson 1999). However, one has to blow up the base locus to get a Lefschetz fibration ...
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Bounding a ratio by its complement [on hold]

Given some integers $n > \beta + \alpha, \beta > \alpha$ and $\alpha > 0$, is there a real number $\delta$ for which $\frac{n-\alpha}{n-\beta} \geq (\frac{\beta}{\alpha})^{\delta}$, where ...
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How to see that this pairing of line bundles is multiplicative?

Given a projective flat morphism $p: X \rightarrow Y$ of integral noetherian schemes of relative dimension one. For a coherent sheaf $F$ on $Y$ we can define a line bundle $det(F)$ on $Y$ and for a ...
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Worst-Case Solution to (Stochastic) Matrix Inequality

EDIT: Some specific conjectures added. This problem comes with an associated stochastic process, but I phrase everything as linear algebra in case somebody from a non-probability community has seen ...
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Reference for a special case of the Hanson-Wright inequality

I would like find tail bounds for the expression \begin{align*} \left|\left\langle a,\phi\right\rangle \left\langle \phi,b\right\rangle -\left\langle a,b\right\rangle\right|, \end{align*} where ...
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maximization of products of two trace function [on hold]

consider the following optimization problem: \begin{array}{l} \mathop {\max }\limits_{\bf{X}} \,\,\,\operatorname{trace}\left( {{\bf{XA}}} \right)\operatorname{trace}\left( {{\bf{XB}}} \right)\\ ...
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Etale Slice Theorem

I found the Luna's Slice Theorem very Technical. It will be helpful if someone illustrates the geometry involved in the theorem. Also why this theorem so useful? This is Luna's Slice theorem from a ...
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Is triple point intersection 'generic' in Teichmuller space?

Let $S$ be a hyperbolic surface of finite type and $\alpha,\beta$ be two closed curves. Consider $X$ to be the set of all those points $\chi$ in the Teichmuller space $\mathcal{T}(S)$ of $S$ such that ...
Cell(J) vs Cof(J) in $\text{sSet}_{\text{Quillen}}$
consider sSet equipped with its Quillen model structure $\text{sSet}_{\text{Quillen}}$, we know that a trivial cofibration is a retract of a transfinite composition of pushouts of horn inclusions. I ...