Related papers: 3-fold log flips according to V.V.Shokurov
This is a survey on the recent fundamental paper by V.V. Shokurov on the existence of log flips.
We piece together ingredients, which are well known and documented in the literature, into a new proof of the existence of semistable 3-fold flips
This is a correction to the afore-mentioned paper in Duke Math. J. vol. 75 (1994), 99-119 by S. Keel, K. Matsuki, and J. McKernan. We completely rewrite Chapter 6 according to the original manuscript of the second author, in order to fix…
We give an upper bound for the minimal discrepancies of hypersurface singularities. As an application, we show that Shokurov's conjecture is true for log-terminal threefolds.
We prove Shokurov's global index conjecture for foliations in dimension at most three. This answers a question of the first author, Meng, and Xie in dimension three. The main result of this paper is partially obtained by generative AI,…
This is an overview article, based on my 2018 Kinosaki lecture, that surveys and announces work on 3-fold flopping contractions, their affine combinatorics, stability conditions, tilting bundles and autoequivalences. Some first applications…
We prove the factoriality of the following nodal threefolds: a complete intersection of hypersurfaces $F$ and $G\subset\mathbb{P}^{5}$ of degree $n$ and $k$ respectively, where $G$ is smooth, $|\mathrm{Sing}(F\cap…
We show that 3-fold terminal flips and divisorial contractions may be factored into a sequence of flops, blow-downs to a smooth curve in a smooth 3-fold or divisorial contractions to points with minimal discrepancies.
The goal of these lecture notes is to present the modern point of view on the classification of Fano threefolds. We tried to offer a self-consistent treatment of the topics covered. \par\medskip\noindent These notes have been published in…
This article is a survey of recent results about scalar curvature and contractible open $3$-manifolds. It is dedicated to the memory of Professor S. S. Chern.
We show that 3-fold terminal flips and divisorial contractions to a curve may be factored by a sequence of weighted blow-ups, flops, blow-downs to a locally complete intersection curve in a smooth 3-fold or divisorial contractions to a…
We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.
We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.
The paper discusses some aspects of Gromov's theory.
We generalise a construction by Prokhorov & Reid of two families of Q-Fano 3-folds of index 2 to obtain five more families of Q-Fano 3-folds; four of index 2 and one of index 3. Two of the families constructed have the same Hilbert series…
Following Shokurov's ideas, we give a short proof of the following klt version of his result: termination of terminal log flips in dimension d implies that any klt pair of dimension d has a log minimal model or a Mori fibre space. Thus, in…
This paper has been withdrawn by the author. The most updated version can be accessed by arXiv:1806.07290.
The aim of these notes is to explain main ideas of the theory of complements. Basically we will follow Shokurov's work alg-geom/9711024.
In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…
This is a revised version (replacing an older one) with typos fixed and the introduction expanded.