41 citations · 270 across the 22 of their papers we have counts for
22 papers
The Nonvanishing problem for varieties with nef anticanonical bundle
Vladimir Lazić, Shin-ichi Matsumura, Thomas Peternell +2
We prove that if is a threefold pair with mild singularities such that is nef, then the numerical class of is effective.
Special MMP for log canonical generalised pairs
Vladimir Lazić, Nikolaos Tsakanikas, with an appendix joint with Xiaowei Jiang
We show that minimal models of -factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we pr…
Special termination for log canonical pairs
Vladimir Lazić, Joaquín Moraga, Nikolaos Tsakanikas
We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.
Birational geometry and the canonical ring of a family of determinantal 3-folds
Vladimir Lazić, Frank-Olaf Schreyer
Few explicit families of 3-folds are known for which the computation of the canonical ring is accessible and the birational geometry non-trivial. In this note we investigate a fami…
Abundance for uniruled pairs which are not rationally connected
Vladimir Lazić
One of the central aims of the Minimal Model Program is to show that a projective log canonical pair with pseudoeffective has a good model, i.e.\ a minimal model $(…
On Nonvanishing for uniruled log canonical pairs
Vladimir Lazić, Fanjun Meng
We prove the Nonvanishing conjecture for uniruled projective log canonical pairs of dimension , assuming the Nonvanishing conjecture for smooth projective varieties in dimension…
A travel guide to the canonical bundle formula
Enrica Floris, Vladimir Lazić
We survey known results on the canonical bundle formula and its applications in algebraic geometry.
On the existence of minimal models for log canonical pairs
Vladimir Lazić, Nikolaos Tsakanikas
We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.
On Generalised Abundance, I
Vladimir Lazić, Thomas Peternell
The goal of this paper is to make a surprising connection between several central conjectures in algebraic geometry: the Nonvanishing Conjecture, the Abundance Conjecture, and the…
On Generalised Abundance, II
Vladimir Lazić, Thomas Peternell
In our previous work, we introduced the Generalised Nonvanishing Conjecture, which generalises several central conjectures in algebraic geometry. In this paper, we derive some surp…
Maps from K-trivial varieties and connectedness problems
Vladimir Lazić, Thomas Peternell
In this paper we study varieties covered by rational or elliptic curves. First, we show that images of Calabi-Yau or irreducible symplectic varieties under rational maps are almost…
On the B-Semiampleness Conjecture
Enrica Floris, Vladimir Lazić
The B-Semiampleness Conjecture of Prokhorov and Shokurov predicts that the moduli part in a canonical bundle formula is semiample on a birational modification. We prove that the re…
The Morrison-Kawamata Cone Conjecture and Abundance on Ricci flat manifolds
Vladimir Lazić, Keiji Oguiso, Thomas Peternell
The aim of this survey paper is threefold: (a) to discuss the status of the Morrison-Kawamata cone conjecture, (b) to report on recent developments towards the Abundance Conjecture…
Abundance for varieties with many differential forms
Vladimir Lazić, Thomas Peternell
We prove that the abundance conjecture holds on a variety with mild singularities if has many reflexive differential forms with coefficients in pluricanonical bundles, assu…
Nef line bundles on Calabi-Yau threefolds, I
Vladimir Lazić, Keiji Oguiso, Thomas Peternell
We prove that a nef line bundle with on a Calabi-Yau threefold with Picard number and with is semiample, that is, some…
A note on the abundance conjecture
Tobias Dorsch, Vladimir Lazić
We prove that the abundance conjecture for non-uniruled klt pairs in dimension implies the abundance conjecture for uniruled klt pairs in dimension , assuming the Minimal Mo…
Automorphisms of Calabi-Yau threefolds with Picard number three
Vladimir Lazić, Keiji Oguiso, Thomas Peternell
We prove that the automorphism group of a Calabi-Yau threefold with Picard number three is either finite, or isomorphic to the infinite cyclic group up to finite kernel and cokerne…
On the number of minimal models of a log smooth threefold
Paolo Cascini, Vladimir Lazić
We give a topological bound on the number of minimal models of a class of three dimensional log smooth pairs of general type.
On the Cone conjecture for Calabi-Yau manifolds with Picard number two
Vladimir Lazić, Thomas Peternell
Following a recent work of Oguiso, we calculate explicitly the groups of automorphisms and birational automorphisms on a Calabi-Yau manifold with Picard number two. When the group…
Finite generation and geography of models
Anne-Sophie Kaloghiros, Alex Küronya, Vladimir Lazić
There are two main examples where a version of the Minimal Model Program can, at least conjecturally, be performed successfully: the first is the classical MMP associated to the ca…
New outlook on the Minimal Model Program, I
Paolo Cascini, Vladimir Lazić
We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective varie…
New outlook on the Minimal Model Program, II
Alessio Corti, Vladimir Lazić
We prove that the finite generation of adjoint rings proved in [Cascini and Lazić] implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Cont…