In this paper results about the Hilbert function and about the number of minimal generators stated in (Orecchia) for disjoint unions of rational smooth curves are generalized to disjoint unions of distinct smooth non special curves. Hence, the maximal rank and the minimal generation of such curves are studied. In particular, we consider elliptic curves and we describe a method to compute their ...

Let k an algebraically closed field, P the n-dimensional projective space over k and TPn the tangent vector bundle of P . In this paper I prove the following result : for every integer l, for every non-negative integer s, if Zs is the union of s points in sufficiently general position in P, then the restriction map H(P, TPn(l)) → H 0(Zs, TPn(l)|Zs) has maximal rank. This result implies that the...

We study the structure of subgroups of minimal connected simple groups of finite Morley rank. We first establish a Jordan decomposition for a large family of minimal connected simple groups including those with a non-trivial Weyl group. We then show that definable, connected, solvable subgroups of such a simple group are the semi-direct product of their unipotent part extended by a maximal toru...

polytope Abstract polytope November, 2013 – p. 2 Abstract polytope Abstract polytope −→ combinatorial generalization of convex polytopepolytope Abstract polytope −→ combinatorial generalization of convex polytope November, 2013 – p. 2 Abstract polytope Abstract polytope −→ combinatorial generalization of convex polytopepolytope Abstract polytope −→ combinatorial generalization of convex polytop...

Recently a correspondence between non-propagating degrees of freedom in maximal supergravity and the very extended algebra E11 has been found. We perform a similar analysis for a supergravity theory with eight supercharges and very extended G2. In particular, in the context of d = 5 minimal supergravity, we study whether supersymmetry can be realised on higher-rank tensors with no propagating d...

• First, the lower bidiagonal matrix A11 with nonzero bidiagonal elements has full column rank and its singular values are simple. Consequently, any zero singular values or repeats that A has must appear in A22. • Second, A11 has minimal dimensions, and A22 has maximal dimensions, over all orthogonal transformations giving the block structure in (2), without any additional assumptions on the st...

Recently a correspondence between non-propagating degrees of freedom in maximal supergravity and the very extended algebra E11 has been found. We perform a similar analysis for a supergravity theory with eight supercharges and very extended G2. In particular, in the context of d = 5 minimal supergravity, we study whether supersymmetry can be realised on higher-rank tensors with no propagating d...

We will give an upper bound of Mordell-Weil rank r for relatively minimal brations of curves of genus g 1 on rational surfaces. Under the assumption that a bration is not locally trivial, we have r 4g+4. Moreover the maximal case (r = 4g + 4) will be studied in detail. We determine the structure of such brations and also the structure of their Mordell-Weil lattices introduced by Shioda.