Related papers: Positivity properties of relative complete interse…
For a local complete intersection morphism, we establish fiberwise denseness in the $n$-dimensional irreducible components of the compactification Nisnevich locally.
This paper introduces an extension of descriptive intersection and provides a framework for descriptive unions of nonempty sets. Fibre bundles provide structures that characterize spatially near as well as descriptively near sets, their…
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…
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 show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of…
We give new characterizations of plurisubharmonic functions and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics. As applications, we present a different method to prove plurisubharmonic variation of…
We introduce a partial positivity notion for algebraic maps via the defect of semismallness. This positivity notion is modeled on $m$-positivity in the analytic setting and $m$-ampleness in the geometric setting. Using this positivity…
In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.
We introduce various probablistic finiteness conditions for profinite groups related to positive finite generation (PFG). We investigate completed group rings which are PFG as modules, and use this to answer a question of Kionke and the…
New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities…
The book is devoted to constructing embedding finite-dimensional maps into trivial bundles and investigating the corresponding general position properties.
We characterize the existence of horizontal path lifts for general connections on arbitrary fiber bundles with a new property that also gives fresh insight into linear and $G$-connections.
In this paper we give some coupled fixed point results for mappings satisfying different contractive conditions on complete partial metric spaces.
We introduce a notion of admissible Hermitian metrics on parabolic bundles and define positivity properties for the same. We develop Chern-Weil theory for parabolic bundles and prove that our metric notions coincide with the already…
We study the space of stability conditions on the total space of the canonical line bundle over the three dimensional projective space. We construct a family of geometric stability conditions and some subset of the boudary of them, which…
For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to…
We study when two projective bundles over two arbitrary smooth projective varieties of different dimensions can be isomorphic. We show that two multi-projective bundles (fibre product of projective bundles) over different projective spaces…
We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.
We predict the conditions under which two oppositely charged membranes show a dynamic, attractive instability. Two layers with unequal charges of opposite sign can repel or be stable when in close proximity. However, dynamic charge density…
Let $X$ be a connected, smooth, and projective curve of genus $g$ over an algebraically closed field of characteristic $p >0$. This paper investigates a characteristic-$p$ analogue of a well-known fact concerning flat vector bundles in…