Related papers: Jet schemes of determinantal varieties

A wide class of exact solutions is obtained for the problem of finding the equilibrium configurations of charged jets of a conducting liquid; these configurations correspond to the finite-amplitude azimuthal deformations of the surface of a…

I illustrate a general formalism based upon the subtraction method for the calculation of next-to-leading order QCD cross sections for any number of jets in any type of hard collisions. I discuss the implementation of this formalism in a…

We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. As particular examples, we explicitly give representatives of all equivalence classes of linear determinantal…

Let X be a geometrically irreducible smooth projective curve over a field k. We describe the algebra of endomorphisms of indecomposable unstable vector bundles over X of rank 2 and degree d. Fixing some numerical invariants, namely the…

The punctual Quot scheme parametrizes all length d quotients of a (locally) trivial rank r sheaf which are supported at a fixed point. The author shows that this scheme is irreducible and (rd-1)-dimensional. The same result was proved…

We prove that the variety defined by the determinant of the matrix of diagonals is $F$-pure for matrices of all sizes and in all positive prime characteristics. Moreover, we find a system of parameters for it.

An experimental research concerning highly underexpanded jets made of different gases from the surrounding ambient is here described. By selecting different species of gases, it was possible to vary the jet-to-ambient density ratio in the…

Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are determined. As a consequence one obtains…

We consider a locally free sheaf $F$ of dimension 2 on $P^2$. A conic $q$ on $P^2$ is called a jumping conic if the restriction of $F$ to $q$ is not the generic one. We prove that the set of jumping conics is the maximal determinantal…

We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…

Complete next-to leading order QCD predictions for (2+1) jet cross sections and jet rates in deep inelastic scattering (DIS) based on a new parton level Monte Carlo program are presented. All relevant helicity contributions to the total…

We prove dimension bounds on the jet schemes of the variety of nilpotent matrices (and of related varieties) in positive characteristic. This result has applications to the analytic properties of the Chevalley map that sends a matrix to its…

On a generic complete intersection surface X^2 in P^4(C) having polynomial equations z^d = R(x,y) and t^e = S(x,y) with 752 <= d <= e <= d^2/648, there exist extrinsic meromorphic jet differentials of the form J(x,y,x',y') / [y^d z^{m(d-1)}…

The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…

We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For relative schemes, we also give a criterion for the nonexistence of semiorthogonal…

We classify the irreducible components of the Hilbert scheme of $n$ points on non-reduced algebraic plane curves, and give a formula for the multiplicities of the irreducible components. The irreducible components are indexed by partitions…

In the space of square matrices, we characterize row-generated subspaces, on which the determinant is an irreducible polynomial. As a corollary, we characterize square systems of polynomial equations with indeterminate coefficients, whose…

We determine the Poincar\'e polynomial of the determinantal variety $\{\det = 0\}$ in the projective space associated with the monoid of $n\times n$ matrices.

Let X be a standard determinantal scheme X \subset \PP^n of codimension c, i.e. a scheme defined by the maximal minors of a t \times (t+c-1) homogeneous polynomial matrix A. In this paper, we study the main features of its normal sheaf…

We construct a determinantal family of quarto-quartic transformations of a complex projective space of dimension $3$ from trigonal curves of degree $8$ and genus $5$. Moreover we show that the variety of $(4,4)$-birational maps of…