Related papers: Jet schemes of toric surfaces (a short version)
In this paper we illustrate an algorithmic procedure which allows to build projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T. The main step of the construction is a combinatorial…
We study arc spaces and jet schemes of generic determinantal varieties. Using the natural group action, we decompose the arc spaces into orbits, and analyze their structure. This allows us to compute the number of irreducible components of…
We construct a positive-dimensional, reducible Severi variety on a toric surface.
This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…
We show that geodesics in the upper half-plane attached to a maximal split torus or a real quadratic torus in $GL_{2, \mathbf{Q}}$ are the only irreducible algebraic curves whose image via the $j$-invariant is contained in an algebraic…
We study the theta divisor of the compactified jacobian of a nodal, possibly reducible, curve. We compute its irreducible components and give it a geometric interpretation consistent with the classical Brill-Noether theory of smooth curves.…
We prove that if X is a locally complete intersection variety, then X has all the jet schemes irreducible if and only if X has canonical singularities. After embedding X in a smooth variety Y, we use motivic integration to express the…
In this manuscript we sharpen the lower bound on the codimension of the irreducible components of the Noether-Lefschetz locus of surfaces in projective toric threefolds given in [BG17]. We also provide a simpler proof of Theorem 4.11 in…
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more generally, rational complex projective surfaces.
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
Breakup of a liquid jet into a chain of droplets is common in nature and industry. Previous researchers developed profound mathematic and fluid dynamic models to address this breakup phenomenon starting from tiny perturbations. However, the…
If two schemes are isomorphic, then their $m$-jet schemes are isomorphic for all $m$. In this paper we consider the converse problem. We prove that if an isomorphism of the $m$-jet schemes is induced from a morphism of the base schemes,…
Let $\mathcal{I}_{d,g,r}$ be the union of irreducible components of the Hilbert scheme whose general points correspond to smooth irreducible non-degenerate curves of degree $d$ and genus $g$ in $\mathbb{P}^r$. We use families of curves on…
We present a new parton level Monte Carlo program for the calculation of jet cross sections in Deep Inelastic Scattering based on Born and next-to-leading order matrix elements. Using a class of invariant jet definition schemes, the program…
We describe, for various degenerations $S\to \Delta$ of quartic $K3$ surfaces over the complex unit disk (e.g., to the union of four general planes, and to a general Kummer surface), the limits as $t\in \Delta^*$ tends to 0 of the Severi…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We study the logarithmic vector bundles associated to arrangements of smooth irreducible curves with small degree on the blow-up of the projective plane at one point. We then investigate whether they are Torelli arrangements, that is, they…
We prove that the Quot-scheme of finite quotients of a vector bundle which are of a given length and supported in one point, is irreducible and of the expected dimension.
We address the modeling dependence of jet taggers built using the method of Mass Unspecific Supervised Tagging, by using two different parton showering and hadronisation schemes. We find that the modeling dependence of the results -…
Consider a finite scheme of length l contained in a smooth quadric surface over the complex numbers. We determine the number of linearly independent curves passing through the scheme, of degree at least l - 1.