Strong -Complements for Semi-Stable Morphisms

  • Stefano Filipazzi

    UCLA, Mathematics Department, Box 951555, Los Angeles, CA 90095-1555, USA
  • Joaquín Moraga

    Department of Mathematics, Princeton University, Fine Hall, Princeton, NJ 08544-1000, USA
Strong $(\delta,n)$-Complements for Semi-Stable Morphisms cover
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We prove the boundedness of global strong -complements for generalized -log canonical pairs of Fano-type. We also prove some partial results towards boundedness of local strong -complements for semi-stable morphisms. As applications, we prove an effective generalized canonical bundle formula for generalized klt pairs and an effective generalized adjunction formula for exceptional generalized log canonical centers. Moreover, we prove that the existence of strong -complements implies a conjecture due to McKernan concerning the singularities of the base of a Mori fiber space.

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Stefano Filipazzi, Joaquín Moraga, Strong -Complements for Semi-Stable Morphisms. Doc. Math. 25 (2020), pp. 1953–1996

DOI 10.4171/DM/790