11 problems

Let $R$ be a local complete Noetherian domain with coefficient field $k$, and set $X:=\operatorname{Spec}R$. For every $n\in\mathbb{N}_0$, consider the $n$-th Nash blowup…

Let $k$ be a field of characteristic zero, let $X$ be a variety of dimension $d$, and let $J\subseteq X$ be the Jacobian subscheme. Denote by $J^{(d-1)}$ its $(d-1)$-th neighborhoo…

Let $K_{\sigma}$ be the intermediate variety in the factorization of the morphism from the Kirwan desingularization $K$ to the desingularization $S$. Narasimhan–Ramanan desingulari…

Let $X$ be an algebraic or analytic variety, and let $X^{\mathrm{nc}}$ denote its normal-crossings locus. A smooth blowing-up is a blowing-up with smooth centre, and it is admissib…

Let $X$ be an algebraic or analytic variety. A smooth blowing-up is a blowing-up with smooth centre, and it is admissible when it satisfies the local normal-crossings and Hilbert–S…

Let $(\overline{X},\varphi_{CS})$ be a nearly $G_2$ conifold with a singularity at $x_0$ modelled on the $G_2$ cone $(C=C(L),\varphi_C)$. An obstruction conjecture for nearly $G_2$…

For sufficiently large $n\in\mathbb{N}$, consider a complete, embedded, noncompact self-shrinker $\Phi_g\subset\mathbb{R}^3$ for mean curvature flow, where $g=2n-1$ denotes its gen…

Let $L_\infty$ be the limiting linear map appearing in the desingularization and obstruction setup, where the theorem was originally stated under the assumption…

Let $(\psi_t)_{t\in(-T,T)}$ be a $1$-parameter family of closed, tamed, definite $4$-forms on $Y$. Let $\hat P$ be an unobstructed singular associative submanifold in $(Y,\psi_0)$…

Strict Bott-Samelson desingularization conjecture. If $w\ngeq v$ for every $v\in\Gamma_n$, then $X^w$ can be desingularized using a sequence of strict Bott-Samelson resolutions.

A $B$-scheme is a scheme $X$ equipped with a boundary $B$; here $(X,B)$ is assumed to be qe and generically reduced, and the scheme has characteristic zero. Write…