Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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A characterization of ACM 0-dimensional schemes in Q.
Get PDFLet X ⊂ Q = P^1 × P^1 be a reduced 0-dimensional subscheme of the quadric Q and let P ∈ X be any point. Using the separating degree of P for X we give a sufficient condition so that X is ACM. This result, together with the previous ones (see [9]) gives a new characterization of ACM 0-dimensional schemes of Q by using separators
Derived Category of toric varieties with Picard number three
Get PDFWe construct a full, strongly exceptional collection of line bundles on the variety X that is the blow up of the projectivization of the vector bundle O_{Pn−1} ⊕ O_{Pn−1}(b_1) along a linear space of dimension n − 2, where b_1 is a non-negative integer
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian
Get PDFWe extend a theorem of Ottaviani on cohomological splitting criterion for vector bundles over the Grassmannian to the case of the symplectic isotropic Grassmanian. We find necessary and sufficient conditions for the case of the Grassmanian of symplectic isotropic lines. For the general case the generalization of Ottaviani’s conditions are sufficient for vector bundles over the symplectic isotropic Grassmannian. By a calculation in the program LiE, we find that Ottaviani’s conditions are necessary for Lagrangian Grassmannian of isotropic k-planes for k ≤ 6, but they fail to be necessary for the case of the Lagrangian Grassmannian of isotropic 7-planes. Finally, we find a related set of necessary and sufficient splitting criteria for the Lagrangian Grassmannian
Adendum to Self-verified extension of affine arithmetic to arbitrary order
No full textLe MatematicheVol. LXIII (2008 - Fasc. I, pp. 15–30)For a technical mistake this article appeared without references and citations. Here we add the references and, page by page, the necessary citations in order of appearance. We apologize for this inconvenient
Betti numbers of powers of ideals
Get PDFLet A=K[x1, ..... ,xn] be a standard graded polynomial ring over a field K, let M = (x_1, .... , x_n) be the graded maximal ideal and I a graded ideal of A. For each i the Betti numbers b_i(I^k ) of I^k are polynomial functions for k>>0. We show that if I is M-primary, then these polynomial functions have the same degree for all i
Enhancement of high-energy distribution tail in Monte Carlo semiconductor simulations using a Variance Reduction Scheme
Get PDFThe Multicomb variance reduction technique has been introduced in the Direct Monte Carlo Simulation for submicrometric semiconductor devices. The method has been implemented in bulk silicon. The simulations show that the statistical variance of hot electrons is reduced with some computational cost. The method is efficient and easy to implement in existing device simulators
Pragmatic 2009
Get PDFThe following six papers arise from the research work done during, and immediately after, the Pragmatic School 2009. This was the eleventh edition of the Pragmatic School, since its starting in 1997, promoted by the Algebraic Geometry group in Catania
Nilpotent groups of semilinear transformations which are monomial
Get PDFLet H be a nilpotent subgroup of ΓL_n (q) = GL_n (q), where φ denotes the field automorfism induced by the Frobenius map. We give a condition on the primes dividing |H ∩ GL_n (q)| under which H is conjugate to a subgroup of the generalized monomial group Diag_n (F∗_q ) Sym(n).We show an application of this result to the determination of Carter subgroups of finite groups.
A note on the Serrin problem in the plane
Get PDFWe investigate the stability of the radial symmetry for the overdetermined Serrin problem in a planar convex set. More precisely, we prove that, whenever we properly perturb both the boundary conditions and the data, then a convex solution is “close” to a suitable paraboloid and the domain is “close” to a ball with respect to the Hausdorff metric
Componentwise linearity of ideals arising from graphs
Get PDFLet G be a simple undirected graph on n vertices. Francisco and VanTuyl have shown that if G is chordal ..