Related papers: Jet schemes of complex plane branches and equising…
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…
It is a challenge for the theoretical particle physicists to perform the phenomenology of the Beyond Standard Model (BSM) theories using advanced simulations which can mimic the experimental environment at the colliders as closely as…
Factorization underpins our ability to make predictions at the LHC, both in Monte Carlo simulations and direct calculations. An improved theoretical understanding of jet substructure can lead to calculations that can confront data and…
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…
We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…
Jets frames, that is a generalisation of ordinary frames on a manifold, are described in a language similar to that of gauge theory. This is achieved by constructing the Cartan geometry of a manifold with respect to the diffeomorphism…
We propose a new geometrical model of matter, in which neutral atoms are modelled by compact, complex algebraic surfaces. Proton and neutron numbers are determined by a surface's Chern numbers. Equivalently, they are determined by…
We investigate the behaviour of jets at high-multiplicity using analytic techniques. We consider in detail the rates, areas and the intermediate splitting scales as a function of the number of jets. In each case, we are able to characterise…
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…
We study high-pt jets from QCD and from highly-boosted massive particles such as tops, W, Z and Higgs, and argue that infrared-safe observables can help reduce QCD backgrounds. Jets from QCD are characterized by different patterns of energy…
In order to make quantitative predictions for jet cross sections in perturbative QCD, it is essential to calculate them to next-to-leading accuracy. This has traditionally been an extremely laborious process. Using a new formalism,…
The degree of a projective subscheme has an upper bound in term of the codimension and the reduction number. If a projective variety has an almost maximal degree, that is, the degree equals to the upper bound minus one, then its Betti table…
We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic. The exponential modality is modelled by composing the…
The present work considers the properties of classes of generally convex sets in the plane known as $1$-semiconvex and weakly $1$-semiconvex. More specifically, the examples of open and closed weakly $1$-semiconvex but non $1$-semiconvex…
We present a constructive procedure, based on the notion of Ap\'ery set, to obtain the value semigroup of a plane curve singularity from the value semigroup of its blow-up and viceversa. In particular we give a blow-down process that allows…
This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising…
We present results on novel analytic calculations to describe invariant mass distributions of QCD jets with three substructure algorithms: trimming, pruning and the mass-drop taggers. These results not only lead to considerable insight into…
The nucleon pair shell model (NPSM) is casted into the so-called M-scheme for the cases with isospin symmetry and without isospin symmetry. The odd system and even system are treated on the same foot. The uncoupled commutators for…
In this paper we give a criterion of irreducibility for a complex power series in two variables, using the notion of jacobian Newton diagrams, defined with respect to any direction. Moreover we study the singularity at infinity of a plane…
We introduce a natural structure of a semigroup (isomorphic to a factorization semigroup of the unity in the symmetric group) on the set of irreducible components of Hurwitz space of marked degree $d$ coverings of $\mathbb P^1$ of fixed…