Related papers: Smoothness and jet schemes
The notion of a spherical space over an arbitrary base scheme is introduced as a generalization of a spherical variety over an algebraically closed field. It is studied how the sphericity condition behaves in families. In particular it is…
We formulate and prove a necessary condition for a sequence of analytic trigonometric polynomials with real non-negative coefficients to be flat a.e.
We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for Q-factorial surfaces and for log canonical surfaces. Moreover, in the…
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative equations. We show that the infinite series obtained by…
We show that a plt surface singularity $(P\in X,B)$ is $F$-liftable if and only if it is $F$-pure and is not a rational double point of type $E_8^1$ in characteristic $p=5$. As a consequence, we prove the logarithmic extension theorem for…
In this paper we prove two results which further classify smoothness properties of Hilbert schemes of points. This is done by counting classes of arrows on Young diagrams corresponding to monomial ideals, building on the approach taken by…
Jet substructure is typically studied using clustering algorithms, such as kT, which arrange the jets' constituents into trees. Instead of considering a single tree per jet, we propose that multiple trees should be considered, weighted by…
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost…
We discuss the arbitrariness in the choice of cutoff scheme in calculations of beta functions. We define a class of "pure" cutoff schemes, in which the cutoff is completely independent of the parameters that appear in the action. In a sense…
We study structural and enumerative aspects of pure simplicial complexes and clique complexes. We prove a necessary and sufficient condition for any simplicial complex to be a clique complex that depends only on the list of facets. We also…
We show that the tame \'etale fundamental group of a connected normal finite type separated scheme remains invariant upon base change between algebraically closed fields of characteristic $p \geq 0$.
We consider smooth plane curves $\mathcal{X}$ of degree $d\geq4$, defined over an algebraically closed field of characteristic $0$, that possess a unique outer Galois point. This geometric condition forces the curve to be a cyclic covering…
We introduce the notion of a neutral representation of a finite group, or finite group scheme, $G$; a representation $V$ with the property that if a gerbe $\mathcal{G}$ over a field $k$ that is a form of the classifying stack $\mathcal{B}…
Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection…
We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any…
In this work, we provide explicit conditions for the coefficients of a symmetric truncated cubic to give a smooth tropical curve. We also examine non-smooth cases corresponding to some specific subdivision types.
We give a criterion to test geometric properties such as Whitney equisingularity and Thom's $a_f$ condition for new families of (possibly non-isolated) hypersurface singularities that "behave well" with respect to their Newton diagrams. As…
Many stellar systems exhibit a finite spatial extent, yet constructing self-consistent spherical models with a prescribed outer boundary is non-trivial because sharp density cutoffs introduce discontinuities that lead to inconsistencies in…
In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing.…
We introduce persistent Betti numbers to characterize topological structure of jets. These topological invariants measure multiplicity and connectivity of jet branches at a given scale threshold, while their persistence records evolution of…