Related papers: A note on flatness of some fiber type contractions
Under some positivity assumptions, extension properties of rationally connected fibrations from a submanifold to its ambient variety are studied. Given a family of rational curves on a complex projective manifold X inducing a covering…
We study in this work flat surfaces with conical singularities, that is, surfaces provided with a flat structure with conical singular points. Finding good parameters for these surfaces in the general case is an open question. We give an…
We present a pair of smooth fiber bundles over the circle with a common $4$-dimensional fiber with the following properties: (1) their total spaces are diffeomorphic to each other; (2) they are isomorphic to each other as topological fiber…
Let $A$ be an abelian variety and $G$ a finite group of automorphisms of $A$ fixing the origin such that $A/G$ is smooth. The quotient $A/G$ can be seen as a fibration over an abelian variety whose fibers are isomorphic to a product of…
We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine…
Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.
Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new…
We construct examples of simply connected surfaces with genus 2 fibrations over the projective line which are of "general type" according to the definition of Campana. These fibrations have special fibres such that the minimum of the…
We develop a formalism that describes the bending and twisting of axoneme-like filament bundles. We obtain general formulas to determine the relative sliding between any arbitrary filaments in a bundle subjected to unconstrained…
We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases, containing both rational and non-rational fibers.
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases,…
Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical…
The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical…
We construct smooth varieties admitting small contractions from arbitrary smooth projective varieties. This construction generalizes Kawamata's four-dimensional example. We also give sufficient conditions for divisors on these varieties to…
This paper is devoted to rigidity of smooth bundles which are equipped with fiberwise geometric or dynamical structure. We show that the fiberwise associated sphere bundle to a bundle whose leaves are equipped with (continuously varying)…
It goes back to Ahlfors that a real algebraic curve admits a real-fibered morphism to the projective line if and only if the real part of the curve disconnects its complex part. Inspired by this result, we are interested in characterising…
If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is…
Let k be an algebraically closed field of characteristic zero. Let f:X-->S be a flat, projective morphism of k-schemes of finite type with integral geometric fibers. We prove existence of a projective relative moduli space for semistable…
In this short note, we will show the following weak evidence of S. Lang conjecture over function fields. Let f : X ---> Y be a projective and surjective morphism of algebraic varieties over an algebraically closed field k of characteristic…