3 problems

Let $(X,x)$ be a 3-dimensional, isolated, non-canonical, log-canonical singularity of embedded dimension 4. Choose an embedding … and let $\boldsymbol{w}=(w_0,w_1,\ldots,w_n)$ be a…

Let $R$ be a regular local ring with a weighted permissible center and consider the associated weighted blow-up with weight vector $(a_1,\ldots,a_n)$, together with strict transfor…

Weighted blow-up bound. Assume $N\geq3$. For every prime divisor $E$ over $A$ with the center at $0$, there exists a prime divisor $F$ obtained by at most $N-1$ weighted blow-ups s…