Related papers: Positivity, singularities, and boundedness
Let $X$ be a smooth projective surface and let $\mathcal{C}$ be an arrangement of curves on $X$. The Harbourne constant of $\mathcal{C}$ was defined as a way to investigate the occurrence of curves of negative self-intersection on blow ups…
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
In this paper we treat some applications of Kawamata's positivity theorem. We get a weak answer to \cite [Section 3]{KeMaMc}. And we investigate the singularities on the target spaces of some morphisms.
This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.
In this work we study neighborhoods of curves in surfaces with positive self-intersection that can be embeeded as a germ of neighborhood of a curve on the projective plane.
The discovery of universe's late-time acceleration and dark energy has overseen a great deal of research into cosmological singularities and in this brief review, we discuss all the prominent developments in this field for the best part of…
The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…
Various contenders for a complete theory of quantum gravity are at odds with each other. This is in particular seen in the ways they relate to information and black holes, and how to effectively treat quantization of the background…
Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms…
We summarize the main ideas of General Relativity and Lorentzian geometry, leading to a proof of the simplest of the celebrated Hawking-Penrose singularity theorems. The reader is assumed to be familiar with Riemannian geometry and point…
We show that any space with a positive upper curvature bound has in a small neighborhood of any point a closely related metric with a negative upper curvature bound.
We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity…
We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…
The problem of classifying boundary points of space-time, for example singularities, regular points and points at infinity, is an unexpectedly subtle one. Due to the fact that whether or not two boundary points are identified or even…
We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior regularity and rigidity properties, in a quantitative and qualitative way, and their (perhaps rather surprising) boundary behavior. We present…
We give conditions for $f$-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.
Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an…
The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…