Related papers: Which circle bundles can be triangulated over $\pa…
We prove that a compact contact threefold which is bimeromorphically equivalent to a Kaehler manifold and not rationally connected is the projectivised tangent bundle of a Kaehler surface.
We characterize when some small Seifert fibered spaces can be the convex boundaries of symplectic rational homology balls and give strong restrictions for others to bound such manifolds. In particular, we show that the only spherical…
It is proven that the partition function of 3-dimensional simplicial gravity has an exponential upper bound with the following assumption: any three dimensional sphere $S^3$ is constructed by repeated identification of neighboring links and…
Raynaud has shown that over a general curve of genus $g \ge 2$, every semistable bundle of rank three and integral slope admits a theta divisor. We show that this can fail for special curves: Over any bielliptic curve of genus $g \ge 5$, we…
We prove that for a given flat surface with conical singularities, any pair of geometric triangulations can be connected by a chain of flips.
In this paper we construct Ulrich bundles of low rank on three-dimensional scrolls (with respect to the tautological line bundle). We pay special attention to the four types of threefold scrolls in $\mathbb{P}^5$ which were classified in…
In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed,…
Let A be the moduli space of (1,p)-polarised abelian surfaces with a level structure, for p an odd prime. Let X be a desingularisation of any algebraic compactification of A. Then X is simply-connected.
Graded vector bundles over a given $\mathbb{Z}$-graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base graded manifold, finitely generated projective graded modules…
A triangulation of a surface is called $q$-equivelar if each of its vertices is incident with exactly $q$ triangles. In 1972 Altshuler had shown that an equivelar triangulation of torus has a Hamiltonian Circuit. Here we present a necessary…
Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate…
We introduce the notion of an \emph{asymptotic triangulation} of the annulus. We show that asymptotic triangulations can be mutated as the usual triangulations and describe their exchange graph. Viewing asymptotic triangulations as limits…
A variety is unirational if it is dominated by a rational variety. A variety is rationally connected if two general points can be joined by a rational curve. This paper aims to show that the two notions can cooperate and, building on…
We provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifolds. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved…
Let $X$ be a connected, compact complex manifold and $S\subset X$ a separating real hypersurface, so that $X$ decomposes as a union of compact complex manifolds with boundary $\bar X^\pm$. Let $\mathcal{M}$ be the moduli space of $S$-framed…
It is known that there are surface bundles of arbitrarily high genus which have genus two Heegaard splittings. The simplest examples are Seifert fibered spaces with the sphere as a base space, three exceptional fibers and which allow…
In this paper, we give a simple proof of a triviality criterion due to I.Biswas and J.Pedro and P.Dos Santos. We also prove a vector bundle on a homogenous space is trivial if and only if the restrictions of the vector bundle to Schubert…
We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of…
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of…
Products of simplices, called simplotopes, and their triangulations arise naturally in algorithmic applications in game theory and optimization. We develop techniques to derive lower bounds for the size of simplicial covers and…