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Q&A for professional mathematicians
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Hottest Questions Today - MathOverflow
Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
Mathoverflow.net news digest
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0 days
I have recently become interested in diffeologies, and more generally smooth sets, and was interested in the notion of a cobordism between two such objects. In order to define such a concept, one would need a way to define the boundary of a diffeology...
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0 days
Constructive proof of uncomputability of the Halting Problem?
There is a proof that not only is the Halting Problem uncomputable, but there is a total computable function $f$ such that, for all Turing machines $M$, $f(M)$ gives an input where $M$ either fails to halt, or halts and gets gets the Halting Problem...
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8 years
Cohomological bounds for scalar curvature of an extremal Kähler metric
There is an interesting trick used in Chen-LeBrun-Weber's paper on the extremal Kähler metrics of $\mathbb{CP}^2\#2\overline{\mathbb{CP}^2}$, and I would like to know whether it can be (has been?) exploited further.
The trick applies to certain Kähler classes $\mathfrak{k}$ of a complex manifold $M$, and allows one to give upper and lower bounds for the scalar curvature of an extremal Kähler metric in $\mathfrak{k}$, if such a metric exists. This is important later... -
0 days
Bounding primes for which the reduction of a Jacobian splits into elliptic curve...
In Corollary 1.5 of this paper, Elkies, Howe, and Ritzenthaler prove that if $C/\mathbb{F}_q$ is a curve of genus $g$ and $g > 510 q^{8\sqrt{q}+3}\log q$, then $\operatorname{Jac}(C)$ cannot be isogenous to a product of elliptic curves.
Now, suppose we specialize to the case where $\operatorname{Jac}(C)$ is isogenous to a power of a supersingular elliptic curve $E/\mathbb{F}_q$. This is equivalent to $C$ being optimal over $\mathbb{F}_{q^2}$, and in this case the maximal possible genus...
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