Extension of Sections via Adjoint Ideals

Extension of Sections via Adjoint Ideals Lawrence Ein and Mihnea Popa

We prove some extension theorems and applications, inspired by the very interesting recent results of Hacon-McKernan [HM1], [HM2] and Takayama [Ta], used in the minimal model program and in turn inspired by fundamental results of Siu. Parts of the proofs we give follow quite closely techniques in [Ka], [HM1], [HM2], and [Laz], which use asymptotic constructions. Some related analytic statements...

Sub-adjoint ideals and hyperplane sections

We study the behaviour of the notion of “sub-adjoint ideal to a projective variety” with respect to general hyperplane sections. As an application we show that the two classical definitions of sub-adjoint hypersurface given respectively by Enriques and Zariski are equivalent.

On One-Sided Ideals of Rings of Linear Transformations

A CHARACTERISTIC p ANALOGUE OF PLT SINGULARITIES AND ADJOINT IDEALS

We introduce a new variant of tight closure and give an interpretation of adjoint ideals via this tight closure. As a corollary, we prove that a log pair (X,∆) is plt if and only if the modulo p reduction of (X,∆) is divisorially F-regular for all large p ≫ 0. Here, divisorially F-regular pairs are a class of singularities in positive characteristic introduced by Hara and Watanabe [HW] in terms...

Local properties of accessible injective operator ideals

In addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a ”good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessib...