Related papers: Models of quadric surface bundles

Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.

It is proved that the number of deformation types of complex structures on a fixed oriented smooth four-manifold can be arbitrarily large. The considered examples are locally simple abelian covers of rational surfaces.

This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.

The exactly solvable four-vertex model on a square grid with the different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model. For the fixed…

We study the moduli space of stable sheaves of Euler characteristic 1, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We give a classification of the stable…

An asymptotic formula is established for the number of rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.

This paper begins with a description of cohomological invariants of non-degenerate quadric bundles, in terms of the cohomology rings of the classifying spaces of the general orthogonal groups. Following this, the Main Theorem of the paper…

Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.

Let $S$ be a regular surface endowed with a very ample line bundle $\mathcal O_S(h_S)$. Taking inspiration from a very recent result by D. Faenzi on $K3$ surfaces, we prove that if $\mathcal O_S(h_S)$ satisfies a short list of technical…

We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.

Using monads, we construct a large class of stable bundles of rank 2 and 3 on 3-fold hypersurfaces, and study the set of all possible Chern classes of stable vector bundles.

We give an explicit formula for Euler characteristics of line bundles on the Hilbert scheme of points on $\mathbb{P}^1\times\mathbb{P}^1$. Combined with structural results of Ellingsrud, G\"ottsche, and Lehn, this determines the Euler…

We show that every plumbing of disc bundles over surfaces whose genera satisfy a simple inequality may be embedded as a convex submanifold in some closed hyperbolic four-manifold. In particular its interior has a geometrically finite…

We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes…

Under a simple assumption on Seifert surfaces, we characterise knots whose stable topological 4-genus coincides with the genus.

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable…

We give examples of surfaces which are Ulrich-wild, i.e. that support families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$.

Generalising work of La Bret\`eche, Browning and Peyre and of the author, we describe the geometry required by Manin's principle and Peyre's conjecture for a family of conic bundle surfaces containing Ch\^atelet surfaces. These surfaces…

We survey some results on real rational surfaces focused on their topology and their birational geometry.

The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen's prediction of characteristic numbers of smooth plane…