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math.AG2024
Toward the classification of threefold extremal contractions with one-dimensional fibers
Shigefumi Mori, Yuri Prokhorov
An extremal curve germ is a germ of a threefold with terminal singularities along a connected reduced complete curve~ such that there exists a -negative contraction $f…
math.AG2023
One-nodal Fano threefolds with Picard number one
Alexander Kuznetsov, Yuri Prokhorov
We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a rel…
math.AG2018
Threefold extremal curve germs with one non-Gorenstein point
Shigefumi Mori, Yuri Prokhorov
An extremal curve germ is the analytic germ of a threefold with terminal singularities along a reduced complete curve admitting a contraction whose fibers have dimension at most on…