All Questions

Let $Y$ be a smooth proper variety over a field $k$, let $X$ be a smooth variety over $k$, $U\hookrightarrow X$ the complement of a strict normal crossing divisor and $\phi\colon U\to Y$ a map. By ...

We consider projective space of dimension $n$ as the parameter space of degree $n$ polynomials in one variable. Then, I am interested in resolving the singularities of the "resultant locus" $...

Let the cyclic group on $n$ elements, $C_n$, act on $\mathbb A^n$ by permuting the co-ordinates (over a field $k$). If $n \neq 0 \in k$, we can resolve the singularities of $X = \mathbb A^n/C_n$ by ...

Since perfectoid techniques have built a bridge between char $0$ and char $p$ worlds, it is conceivable that they can be applied to resolution of singularities in char $p$ using their successful ...

As far as I understand, embedded resolution of singularities means the following: given a variety $X$ over an algebraically closed field, and a closed subvariety $Y$, there exists a birational map $f:...

Let $X={\rm Spec} A$ be a normal affine variety of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$. Also, assume that $S\subset X$ is a prime Weil-divisor on $X$. Now,...