Related papers: Termination of 4-fold canonical flips
A study of certain symplectic $4$-orbifolds with vanishing canonical class is initiated. We show that for any such symplectic $4$-orbifold $X$, there is a canonically constructed symplectic $4$-orbifold $Y$, together with a cyclic orbifold…
We prove the transformation laws of the four Jacobi theta functions using Gordon's proof for the transformation law of the Dedekind eta function.
We prove that for each closed smooth spin 4-manifold M there exists a closed smooth 4-manifold N such that the connected sum M # N admits a conformally flat Riemannian metric.
We describe the closed cone of moving curves of smooth Fano three- and fourfolds by giving finitely many equations that cut out the cone. The equations are induced by the exceptional divisors of divisorial contractions and by nef divisors…
The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…
We give a new proof of Lucas' Theorem in elementary number theory.
In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold…
This replaces the previous version, by correcting an error in the proof of Theorem 1.4, that was pointed out by the referee.
We prove that the generalized rational blowdown, a surgery on smooth 4-manifolds, can be performed in the symplectic category.
We calculate intersection forms of all 4-dimensional almost-flat manifolds
In this paper we survey some finiteness results of the deformation classes of hyperk\"ahler Lagrangian fibrations, and we prove finiteness for stable Lagrangian fibrations with a given discriminant divisor.
We answer the question in the title in the negative by providing four proofs.
We prove the existence of infinite dense free sets (in the usual topology) for set mappings on the reals, under reasonable assumptions.
We introduce the notion of a `canonical' splitting over Z or ZxZ for a finitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken manifold M with incompressible boundary, then the…
A complete description of the deformation classes of real ruled manifolds is given. In particular, we prove that once the complex deformation class is fixed, the real deformation class is prescribed by the topology of the real structure.
We present in this work a new and simple proof of the false centre theorem.
We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
We prove that there exist infinitely many topologically slice knots which cannot bound a smooth null-homologous disk in any definite 4-manifold. Furthermore, we show that we can take such knots so that they are linearly independent in the…
We show that log canonical thresholds satisfy the ACC