On the boundedness of $n$-folds with $κ(X)=n-1$

Abstract

In this note we study certain sufficient conditions for a set of minimal klt pairs (X, ∆) with κ(X, ∆) = dim(X) − 1 to be bounded.

Boundedness of the base varieties of certain fibrations

“…They show the boundedness of the total space under certain assumptions. Filipazzi [16] established the boundedness of varieties with fixed Iitaka volumes whose Iitaka fibrations are elliptic fibrations admitting multisections of fixed degrees. Theorem 1.4 [7,Theorem 1.3].…”

Boundedness of polarised Calabi-Yau fibrations

“…Similarly, the results in [Li20] apply to the study of fibrations of Fano type. The boundedness of varieties with an elliptic fibration is considered in [Bir18], [BDCS20], [CDCH + 18] and [Fil20]. By analogy with the definition of volumes of divisors, the Iitaka volume of a Q-divisor is defined as follows.…”

Boundedness of elliptic Calabi-Yau varieties with a rational section

“…Then by the results of [HMX14] and [Bir18], these conditions imply that Y ′ is bounded and the divisors contracted in the birational map Y Y ′ can be extracted to yield a bounded model Y 1 isomorphic in codimension 1 to Y . These techniques have been recently applied also to the study of the boundedness of ndimensional minimal models of Kodaira dimension n − 1, see [FS20,Fil20a].…”