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There are only one type of Verra fourfold?

I am not aware of Verra fourfolds of second type, and I think the situation with Verra fourfolds is more similar to the situation with GM sixfolds, where also only one type is available.
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Moduli space of Bridgeland semistable objects: what is it?

I recommend D. Huybrechts' Introduction to stability conditions. Moduli spaces, 179–229, London Math. Soc. Lecture Note Ser. 411, Cambridge Univ. Press (2014).

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