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Plus and minus Białynicki-Birula decomposition for normal variety

Yes, \eqref{star} is always a disjoint union (that's obvious). Moreover, each set $X^+(F_k)$ is locally closed and the map $x\mapsto\lim_{t\to0}t\cdot x$ induces an affine morphism $\pi_k:X^+(F_k)\to …
Friedrich Knop's user avatar