Related papers: Perverse obstructions to flat regular compactifica…

Following the work of Totaro and Pereira, we study sufficient conditions under which collections of pairwise-disjoint divisors on a variety over an algebraically closed field are contained in the fibers of a morphism to a curve. We prove…

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in…

We develop further basic tools in the theory of continuous bounded cohomology of locally compact groups. We apply this tools to establish a Milnor-Wood type inequality in a very general context and to prove a global rigidity result which…

Let $\pi : \widetilde{\mathcal{N}} \to \mathcal{N}$ be a Riemannian covering, with $\mathcal{N}$, $\widetilde{\mathcal{N}}$ smooth compact connected Riemannian manifolds. If $\mathcal{M}$ is an $m$-dimensional compact simply-connected…

This is a continuation of math.AG/0609741. Let Y be an affine symplectic variety with a C^*-action with positive weights, and let \pi: X -> Y be its crepant resolution. Then \pi induces a natural map PDef(X) -> PDef(Y) of Kuranishi spaces…

We investigate specific intrinsic curvatures $\rho_k$ (where $1\leq k\leq n$) that interpolate between the minimum Ricci curvature $\rho_1$ and the normalized scalar curvature $\rho_n=\rho$ of $n$-dimensional Riemannian manifolds. For…

First of all, we establish compactness of continuous mappings of the Orlicz--Sobolev classes $W^{1,\varphi}_{\rm loc}$ with the Calderon type condition on $\varphi$ and, in particular, of the Sobolev classes $W^{1,p}_{\rm loc}$ for $p>n-1$…

Let $f : X \to S$ be a smooth projective family defined over $\mathcal{O}_{K}[\mathcal{S}^{-1}]$, where $K \subset \mathbb{C}$ is a number field and $\mathcal{S}$ is a finite set of primes. For each prime $\mathfrak{p} \in…

For $n \geq 1$, the twistor space $\mathfrak{Z}(\mathbb{S}^{2n})$ of the conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the complex Grassmannian manifold $\mathbf{G}(n+1, 2n+2)$, of the set of graphs of…

We formulate a strengthening of the Zariski dense orbit conjecture for birational maps of dynamical degree one. So, given a quasiprojective variety $X$ defined over an algebraically closed field $K$ of characteristic $0$, endowed with a…

Let $W\subset GL(V)$ be a complex reflection group, and ${\mathscr A}(W)$ the set of the mirrors of the complex reflections in $W$. It is known that the complement $X({\mathscr A}(W))$ of the reflection arrangement ${\mathscr A}(W)$ is a…

Zariski decomposition plays an important role in the theory of algebraic surfaces due to many applications. For irreducible symplectic manifolds Boucksom provided a characterization of his divisorial Zariski decomposition in terms of the…

Using currents with minimal singularities, we construct pointwise minimal multiplicities for a real pseudo-effective $(1,1)$-class $\alpha$ on a compact complex $n$-fold $X$, which are the local obstructions to the numerical effectivity of…

We prove a conjecture of Medvedev and Scanlon in the case of regular morphisms of semiabelian varieties. That is, if $G$ is a semiabelian variety defined over an algebraically closed field $K$ of characteristic $0$, and $\varphi\colon G\to…

An algebraic variety is called $\mathbb{A}^{1}$-cylindrical if it contains an $\mathbb{A}^{1}$-cylinder, i.e. a Zariski open subset of the form $Z\times\mathbb{A}^{1}$ for some algebraic variety Z. We show that the generic fiber of a family…

We study closed, connected, spin 4-manifolds up to stabilisation by connected sums with copies of $S^2 \times S^2$. For a fixed fundamental group, there are primary, secondary and tertiary obstructions, which together with the signature…

We show that the Vassiliev invariants of orders $\leq n$ of a knot K, are obstructions to finding a regular Seifert surface, S, whose complement looks "simple" (e.g. like the complement of a disc) to the lower central series of its…

Let $\pi\,:\, X \,\longrightarrow\, Y$ be a finite morphism of smooth projective varieties defined over an algebraically closed field of characteristic zero. We study the necessary and sufficient criteria for $\pi$ such that there exists a…

Motivated by orbifold grand unified theories, we construct a class of three-family Pati-Salam models in a Z6 abelian symmetric orbifold with two discrete Wilson lines. These models have marked differences from previously-constructed…

Two sesquilinear forms $\Phi:\mathbb C^m\times\mathbb C^m\to \mathbb C$ and $\Psi:\mathbb C^n\times\mathbb C^n\to \mathbb C$ are called topologically equivalent if there exists a homeomorphism $\varphi :\mathbb C^m\to \mathbb C^n$ (i.e., a…