Related papers: On semistable Mori contractions

We factorize three-dimensional terminal flops into a composition of divisorial contractions to points and blowing-up smooth curves.

We consider the question whether a real threefold X fibred into quadric surfaces over the real projective line is stably rational (over R) if the topological space X(R) is connected. We give a counterexample. When all geometric fibres are…

A Heegaard splitting of a $3$-manifold is flippable if there is an isotopy that interchanges the two sides of the Heegaard splitting. We explore which Heegaard splittings of Seifert fibered spaces are flippable.

We study from a geographical point of view fibrations of threefolds over smooth curves, such that the general fibre is of general type. We prove the non-negativity of certain relative invariants under general hypotheses and give lower…

We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable…

Motivated by a recent paper of Gabai on the Whitehead contractible 3-manifold, we investigate contractible manifolds $M^n$ which decompose or split as $M^n = A \cup_C B$ where $A,B,C \approx \mathbb{R}^n$ or $A,B,C \approx \mathbb{B}^n$. Of…

We introduce homological and homotopical $r$-syzygies of Mori fibre spaces as a generalization of Sarkisov links and relations of Sarkisov links. For any proper morphism $Y/R$, we construct a contractible (if not empty) CW complex such that…

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…

Given a Q-Cartier divisor $S \subset X$ admitting a fibration $S \rightarrow B$ onto a curve we give sufficient conditions for the existence of a bimeromorphic contraction contracting S onto B. As a corollary we recover a contraction result…

Given a torsion section of a semistable elliptic surface, we prove equidistribution results for the components of singular fibers which are hit by the section, and for the root of unity (identifying the zero component with ${\Bbb C}$) which…

We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric…

This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over the circle. We show that every hyperbolic fibered commensurability…

We present an algorithm for the following problem. Given a triangulated 3-manifold M and a (possibly non-simple) closed curve on the boundary of M, decide whether this curve is contractible in M. Our algorithm runs in space polynomial in…

Local symplectic contractions are resolutions of singularities which admit symplectic forms. Four dimensional symplectic contractions are (relative) Mori Dream Spaces. In particular, any two such resolutions of a given singularity are…

We study constructions of contact forms on closed manifolds. A notion of strong symplectic fold structure is defined and we prove that there is a contact form on $M \x X$ provided that $M$ admits such a structure and $X$ is contact. This…

We survey some of the recent works on the geometry of del Pezzo surfaces over imperfect fields, with applications to 3-dimensional del Pezzo fibrations in positive characteristic. We place particular emphasis on cases where the general…

In a paper published in 2002, the author gave a criterion to determine whether there is a fiber-preserving branched covering between two given orientable Seifert manifolds with orientable bases. Here we supply some details of the proof of…

We focus on a class of Weierstrass elliptic threefolds that allows the base of the fibration to be a Fano surface or a numerically $K$-trivial surface. We define the notion of limit tilt stability, and show that the Fourier-Mukai transform…

In this paper we prove the connectedness of isoperiodic moduli spaces of meromorphic differentials with at least three simple poles on homologically marked smooth curves whose periods are either not contained in a real line, or not…