In this issue of Neuron, three papers, Severi et al. (2014), Thiele et al. (2014), and Wang and McLean (2014), examine the descending circuitry involved in coordinating locomotor behavior in larval zebrafish. Visually evoked locomotor and steering movements in zebrafish are mediated by neurons in the nucleus of the medial longitudinal fascicle (nMLF) that project directly to spinal motoneurons....

E Severi 1 , F Vial 1 , E Peron 2 3 , O Mardh 1 , T Niskanen 1 , J Takkinen 1 1. European Centre for Disease Prevention and Control (ECDC), Stockholm, Sweden 2. European Programme for Intervention Epidemiology Training (EPIET), European Centre for Disease Prevention and Control (ECDC), Stockholm, Sweden 3. Gastrointestinal, zoonosis and tropical diseases unit, Department of infectious diseases ...

Let F be an arbitrary field (of arbitrary characteristic). Let A be a central simple F -algebra endowed with a quadratic pair σ (if charF 6= 2 then σ is simply an orthogonal involution on A). We show that the Witt index of σ over the function field of the Severi-Brauer variety of A is divisible by the Schur index of the algebra A.

Using the Shioda–Tate theorem and an adaptation of Silverman’s specialization theorem, we reduce Mordell–Weil ranks for abelian varieties over fields finitely generated infinite [Formula: see text] to Néron–Severi recently proved by Ambrosi in positive characteristic. More precisely, prove that after a blow-up base surface text], all vertical curves fibration with from complement sparse subset ...

We construct an action of the Neron–Severi part Looijenga–Lunts–Verbitsky Lie algebra on Chow ring Hilbert scheme points a K3 surface. This yields simplification Maulik and Negut’s proof that cycle class map is injective subring generated by divisor classes as conjectured Beauville. The key step in construction explicit formula for Lefschetz duals terms Nakajima operators. Our results also lead...

The topological filtration on the Grothendieck group of the Severi-Brauer variety corresponding to a triquaternion algebra is computed. In particular, it is shown that the second Chow group of the variety is torsionfree. Let F be a field, A a central simple F -algebra of degree 8 and exponent 2, X = SB(A) the Severi-Brauer variety of A [2]. Consider the second Chow group CH(X), i.e. the group o...

In this paper we study the geometry of the Severi varieties parametrizing curves on the rational ruled surface Fn. We compute the number of such curves through the appropriate number of fixed general points on Fn (Theorem 1.1), and the number of such curves which are irreducible (Theorem 1.3). These numbers are known as Severi degrees; they are the degrees of unions of components of the Hilbert...

Let G be a semisimple affine algebraic group of inner type over a field F . We write XG for the class of all finite direct products of projective G-homogeneous F varieties. We determine the structure of the Chow motives with coefficients in a finite field of the varieties in XG. More precisely, it is known that the motive of any variety in XG decomposes (in a unique way) into a sum of indecompo...