Related papers: On the quadratic invariant of binary sextics
We use covariants of binary sextics to describe the structure of modules of scalar-valued or vector-valued Siegel modular forms of degree 2 with character, over the ring of scalar-valued Siegel modular forms of even weight. For a modular…
We investigate the quadratic descent of totally decomposable algebras with involution of orthogonal type in characteristic two. Both separable and inseparable extensions are included.
We evaluate the enumerative invariants of low degree on the mirror quintic threefold.
We obtain an asymptotic formula for the number of $\operatorname{GL}_2(\mathbb{Z})$-equivalence classes of irreducible binary quartic forms with integer coefficients with vanishing $J$-invariant and whose Hessians are proportional to the…
We discuss invariants in equivariant birational geometry.
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated…
We define a new invariant of quadratic Lie algebras and give a complete study and classification of singular quadratic Lie algebras, i.e. those for which the invariant does not vanish. The classification is related to…
We determine the Waring ranks of all sextic binary forms with complex coefficients using a Geometric Invariant Theory approach. Using the five basic invariants for sextic binary forms, our results give a rapid method to determine the Waring…
An alternative construction, using Witt's formalism, of the Arf-invariant of quadratic forms in characteristic 2.
We study the theta map which assigns to a real quadratic form its theta series. We introduce two invariants reflecting whether the differential of the theta map vanishes or is degenerate. We provide examples of lattices where this…
In the space of sextic forms in 4 variables with a decomposition of length 18 we determine and describe a closed subvariety which contains all non-identifiable sextics. The description of the subvariety is geometric, but one can derive from…
An invariant characterization of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space is given in terms of invariants and covariants of a real binary quartic canonically associated to the characteristic…
In this work, we offer a historical stroll through the vast topic of binary quadratic forms. We begin with a quick review of their history and then an overview of contemporary algebraic developments on the subject.
We complete the equisingular deformation classification of irreducible singular plane sextic curves. As a by-product, we also compute the fundamental groups of the complement of all but a few maximizing sextics.
This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.
In this paper we prove a correspondence between a canonical degree six covariant of binary quartic forms $F$ and a cubic covariant of a pair of ternary quadratic forms $(f_A, f_B)$. In the process we obtain a canonical way to diagonalize a…
We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic $3$-space and in de Sitter space. Several dualities of invariants are pointed out.
We present theoretical and numerical evidence for a random matrix theoretic approach to a conjecture about vanishings of quadratic twists of certain L-functions
We give a complete deformation classification of real Zariski sextics, that is of generic apparent contours of nonsingular real cubic surfaces. As a by-product, we observe a certain "reversion" duality in the set of deformation classes of…