Related papers: Surfaces in 4-manifolds: Addendum
In this paper we prove a gap theorem for K\"ahler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author. We also prove a Liouville theorem for…
For each integer $n$ we construct a simply connected $4$-manifold $X$ admitting a smoothly embedded surface $\Sigma$ of self intersection number $n$ such that the complement of the surface has non-trivial fundamental group. This answers a…
We present new smoothing techniques for topologically embedded surfaces in smooth 4-manifolds, which give topological isotopy to a smooth surface. As applications, we prove "topological = smooth" results in dimension 4 for certain disks and…
We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a stabilization result: after adding a fifth trivial sheet two…
In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in a homogeneously regular Riemannian three-manifold, in any…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
This note contains a correction of the proofs of the main results of the paper [A. Yekutieli, Deformation quantization in algebraic geometry, Adv. Math. 198 (2005), 383-432]. The results are correct as originally stated.
We make an attempt at proving the Four Colour Theorem in six pages.
The revised version has two additional references and a shorter proof of Proposition 5.7. This version also makes numerous small changes and has an appendix containing a proof of the degree formula for a parametrized surface.
We give a self-contained introduction to the theory of Turaev's shadows as a tool to study 3 and 4-manifolds. The goal of the present paper twofold: on one side it is intended to be a shortcut to a basic use of the theory of shadows, on the…
In this note, we investigate the relation between double points and complex points of immersed surfaces in almost-complex 4-manifolds and show how estimates for the minimal genus of embedded surfaces lead to inequalities between the number…
We prove the termination of 4-fold canonical flips.
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
In this note, we prove a theorem covering Chartrand, Kaigars, and Lick's theorem in [Proc. Amer. Math. Soc. 32 (1972), 63-68]. As an application, we give a simpler proof of theorem proved by Mader [J. Graph Theory 65 (2010), 61-69. (Theorem…
In this paper, we show the abundance theorem for log canonical surfaces over fields of positive characteristic.
In this appendix we present an expanded version of Section 4 of our paper arXiv:1404.4596, including the proofs of all of the technical lemmas.
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic…
In this note, we point out an error in the proof of Theorem 4.7 of [P. Achar and A.~Henderson, `Orbit closures in the enhanced nilpotent cone', Adv. Math. 219 (2008), 27-62], a statement about the existence of affine pavings for fibres of a…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].