相关论文: Jet schemes and singularities
In this paper we give a complete description of the irreducible components of the jet schemes (with origin in the singular locus) of a two-dimensional quasi-ordinary hypersurface singularity. We associate with these components and with…
We study jet schemes of Newton non-degenerate plane curve singularities. We identify a subgraph of the graph of jet components and show that it can be constructed from walks on the lattice points in the first quadrant of the Cartesian…
We prove a precise inversion of adjunction formula for the log pair associated to a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded from above by…
We prove a result on the inversion of adjunction for log canonical pairs that generalizes Kawakita's result to log canonical centers of arbitrary codimension.
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,…
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…
We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinement of the zero sets of multivariable Alexander polynomials. In particular we identify…
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…
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,…
When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…
We define a certain class of simple varieties over a field $k$ by a constructive recipe and show how to control their (equivariant) truncating invariants. Consequently, we prove that on simple varieties: (i) if $k=\overline{k}$ and…
This article studies the scheme structure of the jet schemes of determinantal varieties. We show that in general, these jet schemes are not irreducible. In the case of the determinantal variety $X$ of $r \times s$ matrices of rank at most…
We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…
We generalize the cosection localized Gysin map to intersection homology and Borel-Moore homology, which provides us with a purely topological construction of the Fan-Jarvis-Ruan-Witten invariants and some GLSM invariants.
In this paper, we discuss a generalization of log canonical singularities in the non-$\mathbb{Q}$-Gorenstein setting. We prove that if a normal complex projective variety has a non-invertible polarized endomorphism, then it has log…
Let $X\subset\mathbb P^{n+1}$ be a smooth complex projective hypersurface. In this paper we show that, if the degree of $X$ is large enough, then there exist global sections of the bundle of invariant jet differentials of order $n$ on $X$,…
Let $G$ be a complex reductive group and $V$ a $G$-module. Then the $m$th jet scheme $G_m$ acts on the $m$th jet scheme $V_m$ for all $m\geq 0$. We are interested in the invariant ring $\mathcal{O}(V_m)^{G_m}$ and whether the map…
In this paper we study singularities in arbitrary characteristic. We propose Finite Determination Conjecture for Mather-Jacobian minimal log discrepancies in terms of jet schemes of a singularity. The conjecture is equivalent to the…
We show how to find a complete set of necessary and sufficient conditions that solve the fixed-parameter local congruence problem of immersions in $G$-spaces, whether homogeneous or not, provided that a certain $k^{\rm th}$ order jet bundle…
We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet…