Invariance of Plurigenera and boundedness for Generalized Pairs

多重亏格的不变性与好的极小模型

Invariance of plurigenera and good minimal models

本文将 Nakayama 关于多重亏格形变不变性的结果推广至正或混合特征 DVR 上的奇异对族，并证明了特定一般型簇好极小模型形变的多重亏格不变性及三维 Gorenstein 典范模型的有界性。

Invariance of plurigenera for generalized polarized pairs with abundant nef parts

We show the invariance of plurigenera for generalized polarized pairs with abundant nef parts and generalized canonical singularities. This is obtained by investigating a type of newly introduced multiplier ideal sheaf which is of bimeromorphic nature.

On invariance of plurigenera for foliations on surfaces

We show that if $(X_t,\mathcal{F}_t)_t$ is a family of foliations with reduced singularities on a smooth family of surfaces, then invariance of plurigenera holds for sufficiently large $m$. On the other hand, we provide examples on which the result fails, for small values of $m$.

Moduli of weighted stable elliptic surfaces and invariance of log plurigenera

This is the third paper in a series of work on weighted stable elliptic surfaces - elliptic fibrations with section and marked fibers weighted between zero and one. Motivated by Hassett's weighted pointed stable curves, we use the log minimal model program to construct compact moduli spaces parameterizing these objects. Moreoever, we show that the domain of weights admits a wall and chamber structure, we describe the induced wall crossing morphisms on the moduli spaces as the weight vector varies, and describe the surfaces that appear on the boundary of the moduli space. The main technical res…

Invariance of plurigenera and Chow-type lemma

This paper answers a question of Demailly whether a smooth family of nonsingular projective varieties admits the deformation invariance of plurigenera affirmatively, and proves this more generally for a flat family of varieties with only canonical singularities and uncountable ones therein being of general type and also two Chow-type lemmata on the structure of a family of projective complex analytic spaces.

Invariance of Plurigenera

The following conjecture on the deformation invariance of plurigenera is proved. For a smooth projective holomorphic family of compact complex manifolds over the open unit 1-disk such that all the fibers are of general type, every plurigenus of the fiber is independent of the fiber. The proof uses Nadel's multiplier ideal sheaves, Skoda's result on the generation of ideals with L2 estimates with respect to a plurisubharmonic weight, and the extension theorem of Ohsawa-Takegoshi-Manivel for holomorphic top-degree forms which are L2 with respect to a plurisubharmonic weight.

Canonical singular hermitian metrics on relative logcanonical bundles

This supersedes 0704.0566. We prove the invariance of logarithmic plurigenera for a projective family of KLT pairs and the adjoint line bundle of KLT line bundles. The proof uses the canonical singular hermitian metrics on relative logcanonical bundles.

Deformations of canonical pairs and Fano varieties

This paper is devoted to the study of various aspects of deformations of log pairs, especially in connection to questions related to the invariance of singularities and log plurigenera. In particular, using recent results from the minimal model program, we obtain an extension theorem for adjoint divisors in the spirit of Siu and Kawamata and more recent works of Hacon and McKernan. Our main motivation however comes from the study of deformations of Fano varieties. Our first application regards the behavior of Mori chamber decompositions in families of Fano varieties: we prove that, in the case…