Related papers: Homological stability and weak approximation
We determine stability boundaries for the wrinkling of highly uni-directionally stretched, finely thin, rectangular elastic sheets. For a given fine thickness and length, a stability boundary here is a curve in the parameter plane, aspect…
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.
This article uses basic homological methods for evaluating examples of compactly supported cohomology groups of line bundles over projective curve.
We study the stability of homological duality properties of Hopf algebras under extensions.
The goal of this short note is to point out that every Fano manifold with a nef tangent bundle possesses an almost K{\"a}hler-Einstein metric, in a weak sense. The technique relies on a regularization theorem for closed positive (1,…
We study quotients of mapping class groups (\Gamma_{g,1}) of oriented surfaces with one boundary component by terms of their Johnson filtrations, and we show that the homology of these quotients with suitable systems of twisted coefficients…
In this paper we give a splitting criterion for uniform vector bundles on Fano manifolds covered by lines. As a consequence, we classify low rank uniform vector bundles on Hermitian symmetric spaces and Fano bundles of rank two on…
We answer a question posed by Morita concerning the non-triviality of certain secondary characteristic classes for surface bundles. In doing so we are naturally led to show that a form of Harer stability holds for surface diffeomorphism…
In this thesis we deal with the specific collective phenomena in condensed matter - striped-structures formation. Such structures are observed in different branches of condensed matter physics, like surface physics or physics of…
Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the…
We give the first examples of flat fiber type contractions of Fano manifolds onto varieties that are not weak Fano, and we prove that these morphisms are Fano conic bundles. We also review some known results about the interaction between…
In this article, we investigate the stability of syzygy bundles corresponding to ample and globally generated vector bundles on smooth irreducible projective surfaces.
We study stability conditions on the derived categories of coherent sheaves on some projective varieties. We give a complete description of the stability manifold for smooth projective curves and we examine a connected open subset of the…
We show that the CM line bundle on a proper family parametrizing specially K-stable varieties with maximal variation is ample. As an application, we show projectivity of any proper subspace of the coarse moduli space of uniformly…
This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…
We discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures,…
We prove a homological stability theorem for moduli spaces of simply-connected manifolds of dimension $2n > 4$, with respect to forming connected sum with $S^n \times S^n$. This is analogous to Harer's stability theorem for the homology of…
Given a line bundle L on a smooth projective curve over the complex numbers, we show that a general extension E of L by the trivial line bundle is very stable: line bundles contained in E have degree much less than half the degree of E.…
A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to moduli spaces of submanifolds of higher…
We give conditions for $f$-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.