All Questions

Is there an analog of the Levi–Civita connection for schemes? There exists algebraic de Rham theory, $n$-forms on vector bundles (algebraically), and familiar constructions from differential geometry....

Let $X\to Y$ be a $C^\infty$ submersion. Consider the following two sheaves. The sheaf on $Y$ comprised of jets of sections of $X\to Y$. The sheaf on $X$ given by the quotient of $\Delta_{X/Y}^{-1}C^\...

Let $M$ be a manifold. Let $G$ be a Lie group and $\mathfrak{g}$ be its Lie algebra. Let $P(M,G)$ be a principal bundle. Recall that, a connection on $P(M,G)$ is a distribution $\mathcal{H}\subseteq ...

Let $(X,\omega)$ be a compact K"ahler manifold of dimension $n$, and let $D=\sum_{i=1}^r D_i$ be a simple normal crossing divisor on it, i.e., a divisor with smooth components $D_i$ intersecting ...