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Register a new userOn a generalized canonical bundle formula for generically finite morphisms
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We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with $mathbb{R}$-coefficients). This complements Filipazzis canonical bundle formula for morphisms with connected fibres. It is then applied to obtain a subadjunction formula for log canonical centers of generalized pairs. As another application, we show that the image of an anti-nef log canonical generalized pair has the structure of a numerically trivial log canonical generalized pair. This readily implies a result of Chen--Zhang. Along the way we prove that the Shokurov type convex sets for anti-nef log canonical divisors are indeed rational polyhedral sets.
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The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered in this paper is a weaker version of the usual nonvanishing conjecture, but valid in the more general setting of generalized log canonical pairs. We confirm it in dimension two. Under some necessary conditions we obtain effecti
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