Related papers: Jet Schemes, Newton Polygons and Continued Fractio…
In this paper, we characterize all curves over $\mathbb{F}_q$ arising from a plane section $$ \mathcal{P} : X_3-e_0X_0-e_1X_1-e_2X_2 = 0 $$ of the Fermat surface $$ \mathcal{S} : X_0^d + X_1^d + X_2^d +X_3^d = 0, $$ where $q = p^{h} = 2d+1$…
The splice quotients are an interesting class of normal surface singularities with rational homology sphere links, defined by W. Neumann and J. Wahl. If Gamma is a tree of rational curves that satisfies certain combinatorial conditions,…
We study logarithmic jet schemes of a log scheme and generalize a theorem of M. Mustata from the case of ordinary jet schemes to the logarithmic case. If X is a normal local complete intersection log variety, then X has canonical…
For an arrangement $\mathcal{H}$ of hyperplanes in $\mathbb{R}^n$ through the origin, a region is a connected subset of $\mathbb{R}^n\setminus\mathcal{H}$. The graph of regions $G(\mathcal{H})$ has a vertex for every region, and an edge…
Constructions and exploration of plane algebraic curves has received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. We use them to explore the…
We introduce a graph structure on Euclidean polytopes. The vertices of this graph are the $d$-dimensional polytopes contained in $\mathbb{R}^d$ and its edges connect any two polytopes that can be obtained from one another by either…
We show that the resolution graph of a plane curve singularity admits a canonical decomposition into elementary graphs.
All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via tangent directions with rational norm, this includes the important case of rational Pythagorean hodograph curves. We study vector subspaces…
Jet clustering is traditionally an unsupervised learning task because there is no unique way to associate hadronic final states with the quark and gluon degrees of freedom that generated them. However, for uncolored particles like $W$, $Z$,…
We train a network to identify jets with fractional dark decay (semi-visible jets) using the pattern of their low-level jet constituents, and explore the nature of the information used by the network by mapping it to a space of jet…
Let $M^3 \subset \mathbb{C}^2$ be a $\mathcal{C}^\omega$ Levi nondegenerate hypersurface. In the literature, Cartan-Moser chains are detected from rather advanced considerations: either from the construction of a Cartan connection…
We define a derived enhancement of the hyperquot scheme (also known as nested Quot scheme), which classically parametrises flags of quotients of a perfect coherent sheaf on a projective scheme. We prove it is representable by a derived…
The process by which jet algorithms construct jets and subjets is inherently ambiguous and equally well motivated algorithms often return very different answers. The Qjets procedure was introduced by the authors to account for this…
The theory of relative logarithmic jet spaces is developed for log schemes. With this theory the existence of bounds of intersection multiplicities of curves and divisors on certain log schemes is established. This result extends those of…
We show the existence of toric resolution tower for an irreducible curve singularity which is explicitly described by Tschirnhausen polynomials. We deduce for a smooth affine plane curve from its topology restrictions for its singularity at…
Some topics in the theory of jets are reviewed. These include jet precession, unconfined jets, the origin of knots, the internal shock model as a unifying theme from protostellar jets to Gamma-ray bursts, relations between the…
Parsec scale jet properties are shortly presented and discussed. Observational data are used to derive constraints on the jet velocity and orientation, the presence of velocity structures, and the connection between the pc and kpc scale.…
Unfolding, for example of distortions imparted by detectors, provides suitable and publishable representations of LHC data. Many methods for unbinned and high-dimensional unfolding using machine learning have been proposed, but no…
Generalizing pseudospherical drawings, we introduce a new class of simple drawings, which we call separable drawings. In a separable drawing, every edge can be closed to a simple curve that intersects each other edge at most once. Curves of…
In 1985 Joe Harris proved the long standing claim of Severi that equisingular families of nodal plane curves are irreducible whenever they are non-empty. For families with more complicated singularities this is no longer true. Given a…