Related papers: An explicit expression of the Luroth invariant
We present an explicit method that, given a generic tuple of Dixmier-Ohno invariants, reconstructs a corresponding plane quartic curve.
In this paper we consider plane quartics with to involutions. We compute the Dixmier invariants, the bitangents and the Matrix representation problem of these curves, showing that they have symbolic solutions for the last two questions.
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
A formula is given for the Seiberg-Witten invariants of a 4-manifold that is cut along certain kinds of 3-dimensional tori. The formula involves a Seiberg-Witten invariant for each of the resulting pieces.
We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.
We construct explicit closed GL(2, R)-invariant loci in strata of meromorphic differentials of arbitrary large dimension with fully degenerate Lyapunov spectrum. This answers a question of Forni-Matheus-Zorich.
Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called L\"uroth quartics. The locus of singular L\"uroth quartics has two irreducible components, both of codimension two in $\P^{14}$. We compute…
We give an explicit slice formula for a surface invariant of generic immersions in $\mathbb{R}^3$, expressed in terms of curve invariants arising from planar slices. Using a motion-picture viewpoint, we introduce differential measures that…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
We give a complete factorization of the invariant factors of resultant matrices built from birational parameterizations of rational plane curves in terms of the singular points of the curve and their multiplicity graph. This allows us to…
We describe explicit algorithms for factoring q-difference operators and solving q-difference equations. These are well known results, presented in a "concrete" form. ----- Nous decrivons des algorithmes explicites pour la factorisation…
In this paper we determine the conductor exponent of non-special Ciani quartics at primes of potentially good reduction in terms of the Ciani invariants. As an intermediate step in order to do so, we provide a reconstruction algorithm to…
We provide an explicit algorithm to calculate invariant tensors for the adjoint representation of the simple Lie algebra $sl(n)$, as well as arbitrary representation in terms of roots. We also obtain explicit formulae for the adjoint…
Explicit generators are given for the ring of invariant polynomials under the coadjoint representation of certain inhomogeneous groups.
In this paper we characterize the closed invariant subspaces for the ($*$-)multiplier operator of the quaternionic space of slice $L^2$ functions. As a consequence, we obtain the inner-outer factorization theorem for the quaternionic Hardy…
This short article presents explicit expressions for roots of a quartic equation that has all four real roots. Although a general expression for quartic roots is available on Wikipedia, an optimized and slightly shorter expression for only…
The proof of the theorem concerning to the inverse cyclotomic Discrete Fourier Transform algorithm over finite field is provided.
A large class of polarized and unpolarized deep inelastic data is successfully described with Fermi-Dirac functions for the non-diffractive part of quark parton distributions. The NLO approach used here improves the agreement with…
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…
We describe explicitly the algebra of polynomial functions on the Hilbert space of four qubit states which are invariant under the SLOCC group $SL(2,{\mathbb C})^{4}$. From this description, we obtain a closed formula for the…