Related papers: Une remarque sur l'invariant de Arf

This paper generalizes the bordered-algebraic knot invariant introduced in an earlier paper, giving an invariant now with more algebraic structure. It also introduces signs to define these invariants with integral coefficients. We describe…

Counting integral binary quadratic forms with certain restrictions is a classical problem. In this paper, we count binary quadratic forms of fixed discriminant given restrictions on the size of their coefficients. We accomplish this by…

This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…

Let k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack \hat G over k, the metaplectic extension of the Greenberg realization of Sp_{2n}(R). We also…

In this paper we determine the group of rational automorphisms of binary cubic and quartic forms with integer coefficients and non-zero discriminant in terms of certain quadratic covariants of cubic and quartic forms. This allows one to…

The simultaneous invariants of 2, 3, 4 and 5 ternary quadratic forms under the group $\SL(3, {\Bbb C})$ were given by several authors (P. Gordan, C. Ciamberlini, H.W. Turnbull, J.A Todd), utilizing the symbolic method. Using the Jordan…

For a field extension $L/K$ we consider maps that are quadratic over $L$ but whose polarisation is only bilinear over $K$. Our main result is that all such are automatically quadratic forms over $L$ in the usual sense if and only if $L/K$…

We introduce an invariant of varieties in positive characteristic which generalizes the a-number of an abelian variety. We calculate it in some examples and discuss its meaning for moduli.

Looking in positive characteristic for failures of the Bertini-Sard theorem, we determine, up to birational equivalence, the separable proper morphisms of smooth algebraic varieties in characteristic two, whose fibres are non-smooth curves…

We revisit the notion of one-sided recognizability of morphisms and its relation to two-sided recognizability.

We discuss some new invariants of quark mixing and show their usefulness with a simple example. We also present some other new tools for analyzing quark mixing.

In this paper, we show that the \alpha_{m,2}-invariant of a smooth cubic surface with Eckardt points is strictly bigger than 2/3. This can be used to simplify Tian's original proof of the existence of Kaehler-Einstein metrics on such…

We give an estimate of exponential sums over singular binary quintic forms in a characteristic-free form, based on the Waring decomposition of binary forms. This extends the method on our preceding result on the space of binary quartics to…

Some binary quadratic operads are endowed with anticyclic structures and their characteristic functions as anticyclic operads are determined, or conjectured in one case.

We construct canonical $\mathbb{Q}$-factorial Gorenstein affine fourfolds in every positive characteristic that are not quasi-$F$-split.

We study invariant Hermitian forms on a conformal vertex algebra and on their (twisted) modules. We establish existence of a non-zero invariant Hermitian form on an arbitrary $W$-algebra. We show that for a minimal simple $W$-algebra…

We discuss certain representations of GL 2 Fq[T] in equal characteristic and associated vectorial modular forms

An algebraic deformation theory of coalgebra morphisms is constructed.

Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can…

Let $p$ and $q$ be anisotropic quadratic forms of dimension $\geq 2$ over a field $F$. In a recent article, we formulated a conjecture describing the general constraints which the dimensions of $p$ and $q$ impose on the isotropy index of…