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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

1 vote
0 answers
169 views

When the action of reductive group on algebraic variety is not equidimensional?

I saw the question When is an almost geometric quotient flat? which said "The quotient $\pi$ is flat if and only if $\pi$ is equidimensional and $X$ is smooth". I am curious is there an example that …
0 votes
1 answer
178 views

Hypersurface on $\mathbb{P}^m\times\mathbb{P}^n$ [closed]

I have found a statement (Harris "Algebraic Geometry", p.269) saying that a hypersurface in $\mathbb{P}^m\times\mathbb{P}^n$ can be written as a single equation. I couldn't find the proof. How can I …