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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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Is $X\times \mathbb{P}^{n}$ connected for a smooth, proper and connected scheme $X$?
Let $S$ be a base-scheme, for our purposes we can assume it is the spectrum of a field $k$.
Given a smooth, proper and connected $S$-scheme $X$ and an integer $n\geq 1$,
is then the fibre-product $X\t …