Complements on log surfaces

Kudryavtsev, Sergey Alexsandrovich

doi:10.1070/sm2004v195n06abeh000828

Cited by 3 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [Bir04], Birkar proved the existence of bounded (δ, n)-complements for surfaces. Kudryavtsev used the theory of complements to study log del Pezzo surfaces with no discrepancy less than − 6 7 [Kud04], and Kudryavtsev and Fedorov classified non-Q-complemented surfaces [KF04]. In [PS09], Prokhorov and Shokurov proved that boundedness of (0, n)-complements follows from the conjecture of effective adjunction and the Borisov-Alexeev-Borisov conjecture (or BAB conjecture for short).…”

Section: Introductionmentioning

confidence: 99%

Strong $(\delta,n)$-Complements for Semi-Stable Morphisms

Filipazzi

Moraga

2020

Doc. Math.

View full text Add to dashboard Cite

We prove the boundedness of global strong (δ, n)complements for generalized ǫ-log canonical pairs of Fano-type. We also prove some partial results towards boundedness of local strong (δ, n)-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 (δ, n)-complements implies a conjecture due to McKernan concerning the singularities of the base of a Mori fiber space.

show abstract

Section: Introductionmentioning

confidence: 99%

Strong $(\delta,n)$-Complements for Semi-Stable Morphisms

Filipazzi

Moraga

2020

Doc. Math.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Strong $(δ,n)$-complements for semi-stable morphisms

Filipazzi,

Moraga

2018

Preprint

View full text Add to dashboard Cite

We prove boundedness of global strong (δ, n)-complements for generalized ǫ-log canonical pairs of Fano type. We also prove some partial results towards boundedness of local strong (δ, n)-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 (δ, n)-complements implies a conjecture due to M c Kernan concerning the singularities of the base of a Mori fiber space.

show abstract