Related papers: Surface bundles over surfaces with arbitrarily man…

We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det(E)$). This result is a higher-rank version of a theorem…

We show that there is a good notion of irreducible sympelectic varieties of $\mathrm{K3}^{[n]}$-type over an arbitrary field of characteristic zero or $p > n + 1$. Then we construct mixed characteristic moduli spaces for these varieties.…

Let $X$ be a rational elliptic surface with elliptic fibration $\pi:X\to\Bbb{P}^1$ over an algebraically closed field $k$ of any characteristic. Given a conic bundle $\varphi:X\to\Bbb{P}^1$ we use numerical arguments to classify all…

We establish the existence of models of quadric surface bundles with prescribed \'etale local forms.

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…

A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet…

Let $M$ be a compact 3-manifold with a triangulation $\tau$. We give an inequality relating the Euler characteristic of a surface $F$ normally embedded in $M$ with the number of normal quadrilaterals in $F$. This gives a relation between a…

We consider elliptic curves whose coefficients are degree 2 polynomials in a variable t. We prove that for infinitely many values of t the resulting elliptic curve has rank at least 1. All such curves together form an algebraic surface…

Given a fiber bundle, we construct a differential graded Lie algebra model for the classifying space of the monoid of homotopy equivalences of the base covered by a fiberwise isomorphism of the total space.

Edge bundling is an important concept heavily used for graph visualization purposes. To enable the comparison with other established near-planarity models in graph drawing, we formulate a new edge-bundling model which is inspired by the…

This note corrects a mistake in Theorem~4.1 of https://doi.org/10.1016/j.aim.2021.107598 (arXiv:1901.03395). The error noted here does not affect any other results of loc. cit. To correct the error, here I prove a more general result…

Werner Meyer constructed a cocycle in $H^2(Sp(2g, \mathbb{Z}); \mathbb{Z})$ which computes the signature of a closed oriented surface bundle over a surface, with fibre a surface of genus g. By studying properties of this cocycle, he also…

In this paper we give a gauge theoretic construction of the joint moduli space of stable G-Higgs bundles on closed Riemann surfaces, where the Riemann surface structure is allowed to vary in the Teichm\"uller space of the underlying smooth…

We study the question when a manifold that fibers over a sphere can be rationally essential, or even have positive simplicial volume. More concretely, we show that mapping tori of manifolds (whose fundamental groups can be quite arbitrary)…

Let $S$ be a geometrically ruled surface with invariant $e$ on a curve $C$. We deal with Ulrich line bundles and $\mu$-stable special Ulrich bundles of rank $2$ on $S$ when $e\ge0$, slightly extending a recent result due to M. Aprodu, L.…

A linear system on a smooth complex algebraic surface gives rise to a family of smooth curves in the surface. Such a family has a topological monodromy representation valued in the mapping class group of a fiber. Extending arguments of…

Using the techniques introduced by Corvaja and Zannier we solve the non-split case of the geometric Lang-Vojta Conjecture for affine surfaces isomorphic to the complement of a conic and two lines in the projective plane. In this situation…

We construct infinitely many examples of macroscopically large manifolds of dimension $m \geq 4$ equipped with circle bundles whose total spaces admit metrics of positive scalar curvature and have macroscopic dimension at most $\lceil m/2…

We show that a smooth 1-parameter family of foliations by circles of a closed 3-manifold, deforming the foliation whose leaves are the fibers of a circle bundle, is trivial, i.e. all the foliations of the family arise from circle bundles…

We demonstrate an obstruction to finding certain splittings of four-manifolds along sufficiently twisted circle bundles over Riemann surfaces, arising from Seiberg-Witten theory. These obstructions are used to show a non-splitting result…