3 problems
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Openness conjecture for birational rigidity in families of Mori fibrations
Openness conjecture for birational rigidity. The set
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Classification of smooth Mori fibrations birational to the double cone variety
Classification conjecture. Any smooth Mori fibration birational to is biregular to either or for some curve .
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Landau–Ginzburg families conjecture for Sarkisov links
A Sarkisov link is a birational map, or birational cobordism, connecting two Mori fibrations. Landau–Ginzburg families conjecture. One-parameter families of Landau–Ginzburg models…