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A geometry question that I thought about more seriously a few years ago... thought it'd be a good first question for MO. I'm aware that there are a number of Torelli type theorems now proven for ...

Let $X$ be a complex manifold, $Y\hookrightarrow X$ a complex compact submanifold. Let $T_{X/Y}$ denote the normal bundle of $Y$ in $X$, and $\mathcal{O}(T_{X/Y})$ its sheaf of holomorphic sections. ...

As proposed by Quillen, Drinfeld, and Deligne and other important mathematicians, there is supposed to be a philosophy that, at least over a field of characteristic zero, assigns to every "deformation ...

Let $\mathcal{M},\mathcal{F}$ be the classifiying spaces (i.e. complex manifolds) of two (possibly) different moduli problem. To give a map $$f:\mathcal{M}\rightarrow \mathcal{F}$$ means that for each ...

This is a question related to Semistable curves of genus $g\geq 2$ form an Artin algebraic stack in the etale topology? Let $\mathcal C\rightarrow \mathcal M^{ss}_g$ be the universal curve over the ...