Questions tagged [resolution-of-singularities]
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Resolution of singularities for flat families.
Is there a resolution of singularities for flat families?
More precisely, if $X \rightarrow \mathbb{A} ^n$ is a flat map, does there exist a map $Y \rightarrow X$ such that, for every $p \in \mathbb{...
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Hironaka's proof of resolution of singularities in positive characteristics
Recent publication of Hironaka seems to provoke extended discussions, like Atiyah's proof of almost complex structure of $S^6$ earlier...
Unlike Atiyah's paper, Hironaka's paper does not have a ...
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Equivariant resolution of singularities
I am looking for some references on equivariant resolution of singularities. In most references quoted on mathoverflow (for instance : Reference on an equivariant resolution of singularities), they ...
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Can we foliate the punctured space by tori?
Is it possible to have a 2 dimensional foliation of $\mathbb{R}^{3}-\{0\}$ such that each leaf is homeomorphic to the torus? what algebraic topological obstruction exist?
Another question: is there ...
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Singularities of fibrations
Let $f:X\rightarrow \mathbb{P}^2$ be a fibration, here $X$ is a projective variety of dimension three.
Assume that there exixts a smooth curve $C\subset\mathbb{P}^2$ such that for any $p\in\mathbb{P}...
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Cone over the Veronese surface
Let $V\subset\mathbb{P}^5$ be the Veronese surface and let $X\subset\mathbb{P}^6$ be the cone over it. Since $X$ is $\mathbb{Q}$-factorial there are two integers $a,b$ such that $aK_X = \mathcal{O}_X(...
user56259
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Intuition behind RDP (Rational Double Points)
Let $S$ be a surface (so a $2$-dimensional proper $k$-scheme) and $s$ a singular point which is a rational double point.
One common characterisation of a RDP is that under sufficient conditions there ...
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Are the fibers of this morphism geometrically regular?
Let $A\rightarrow B$ be a local morphism of complete noetherian rings making $B$ a formally smooth $A$-algebra. Does the induced morphism $\textrm{Spec}(B)\to\textrm{Spec}(A)$ have geometrically ...
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Locally toric resolutions of compactifications
Suppose $U$ is a smooth, open $n$-dimensional variety over $\mathbb{C}.$ Say $X, X'$ are two proper normal-crossings compactifications of $U$. Call a map $m: X'\to X$ a modification if it is an ...
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Strict transform under resolution of singularity along a singular $\mathbb{Q}$-Cartier divisor
$\DeclareMathOperator\Bl{Bl}$Let $f: Y=\Bl_0^\omega(\mathbb{C}^3)\to \mathbb{C}^3$ be a weighted blow up of $\mathbb{C}^3$ with weights $w(x,y,z)=(1,1,2)$. Then $Y$ and the exceptional divisor $E\cong ...
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