9 problems

Semi-supermanifold semi-transition conjecture. On $U_\alpha\cap U_\beta$,

Increasing-chain conjecture. If $F$ is $n$-representable, then

Onishchik's conjecture. These more general symmetries are no less reasonable than the conventional symmetries infinitesimally embodied by Lie superalgebras.

Let $(\mathcal{U}, \vartheta)$ be an algebraic deformation of a super Riemann surface $S(C, T^*_{C, -})$ over $\mathbb{A}^{0|n}_\mathbb{C}$. Its primary obstruction…

Let $(X,T^*_{X,-})$ be a model and let $(Y,T^*_{Y,-})$ be a $gt$-model over a connected Stein base whose fiber is $(X,T^*_{X,-})$, so that $Y=X\times B$ and…

Let $(Y,T^*_{Y,-})$ be a $gt$-model. The secondary obstruction complex has differentials … Let $\Theta(T^*_{Y,-})$ denote the model class and let…

Let $M$ be a complex manifold and $E\rightarrow M$ a holomorphic vector bundle of rank $q$. Write … For each $j$, let $\mathfrak{M}_{(M,E)}^{(j);\mathrm{triv.}}$ denote the moduli…

A supermanifold is a local ringed space modeled on open domains of $\mathbb R^{p}$ endowed with the $\mathbb Z_{2}$-graded algebra … The coordinate description uses local charts an…

Existence conjecture. Similar formulas should be obtainable for symbols of higher order, and a natural projectively invariant quantization should exist when $n-m=-1$. The case…