Related papers: Termination of 4-fold canonical flips
We show that finite Galois extensions with cyclic Galois group are radical.
We study smoothings of Fano threefolds. We prove that the Picard number remains constant in the case of terminal Gorenstein singularities.
We prove that termination of lower dimensional flips for generalized klt pairs implies termination of flips for log canonical generalized pairs with a weak Zariski decomposition. Moreover, we prove that the existence of weak Zariski…
We prove that any closed simply-connected smooth 4-manifold is 16-fold branched covered by a product of an orientable surface with the 2-torus, where the construction is natural with respect to spin structures. In particular this solves…
We present a few general results on foliations of 4-manifolds by surfaces: existence, tautness, relations to minimal genus of embedded surfaces; as well as some open problems. We hope to stimulate interest in this area.
In this paper we describe the classification of all the geometric fibrations of a closed flat Riemannian 4-manifold over a 1-orbifold.
We prove several extensions of the Erdos-Fuchs theorem.
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
We prove the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical $4$-folds.
We give a new proof of the main theorem in the theory of C(6) small cancellation complexes. We prove the fundamental theorem of cubical small cancellation theory for C(9) cubical small cancellation complexes.
We prove a result on the existence of linear forms of a given Diophantine type.
We prove a characterization of Fano type varieties.
Examples are given to show that some compact contractible 4-manifolds can be knotted in the 4-sphere. It is then proved that any finitely presented perfect group with a balanced presentation is a knot group for an embedding of some…
We prove Faltings Finiteness Theorem using Rieffel's classification of the noncommutative tori.
Reconstruction theorem for the Moufang loops is proved.
We show that the number of equivariant deformation classes of real structures in a given deformation class of compact hyperkahler manifolds is finite.
We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss…
We prove a diagonalisation theorem for the tautological, or generalised Miller-Morita-Mumford classes of compact, smooth, simply-connected definite $4$-manifolds. Our result can be thought of as a families version of Donaldson's…
We prove that a contractible orbifold is a manifold.
We prove that a weak $\mathbb{Q}$-Fano $3$-fold with terminal singularities has unobstructed deformations. By using this result and computing some invariants of a terminal singularity, we provide two results on global deformation of a weak…