Projective normality of model varieties and related results

We prove that the multiplication of sections of globally generated line bundles on a model wonderful variety M of simply connected type is always surjective. This follows by a general argument which works for every wonderful variety and reduces the study of the surjectivity for every couple of globally generated line bundles to a finite number of cases. As a consequence, the cone defined by a complete linear system over M or over a closed G-stable subvariety of M is normal. We apply these results to the study of the normality of the compactifications of model varieties in simple projective spaces and of the closures of the spherical nilpotent orbits. Then we focus on a particular case proving two specific conjectures of Adams, Huang and Vogan on an analogue of the model orbit of the group of type E8.Comment: v2: 54 pages, new introduction and several minor changes, added Proposition 9.2. To appear on Representation Theor

Spherical nilpotent orbits and abelian subalgebras in isotropy representations

Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy representation of $G_0$. Given an abelian subalgebra $\mathfrak a$ of $\mathfrak g$ contained in $\mathfrak g_1$ and stable under the action of some Borel subgroup $B_0 \subset G_0$, we classify the $B_0$-orbits in $\mathfrak a$ and we characterize the sphericity of $G_0 \mathfrak a$. Our main tool is the combinatorics of $\sigma$-minuscule elements in the affine Weyl group of $\mathfrak g$ and that of strongly orthogonal roots in Hermitian symmetric spaces.Comment: Latex file, 29 pages, minor revision, to appear in Journal of the London Mathematical Societ

Nilpotent orbits of height 2 and involutions in the affine Weyl group

Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B be a Borel subgroup of G. Then B acts with finitely many orbits on the variety N_2 of the nilpotent elements in g whose height is at most 2. We provide a parametrization of the B-orbits in N_2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g.Comment: v2: 28 pages, 1 table. Minor revision. To appear in Indag. Mat

Some combinatorial properties of skew Jack symmetric functions

Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a $\pi$ angle of the skew diagram. It follows that, in some special cases, the coefficients of the skew Jack symmetric functions with respect to the basis of the monomial symmetric functions are polynomials with nonnegative integer coefficients

Nilpotent orbits of height 2 and involutions in the affine Weyl group

Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B G be a Borel subgroup. Then B acts with finitely many orbits on the variety N2 of the nilpotent elements whose height is at most 2. We provide a parametrization of the B-orbits in N2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g

La Gestione dei trasporti in emergenza: attività, prodotti e risultati dell'esercitazione nazionale di Protezione Civile in Valtellina

L'articolo riporta l’esperienza maturata dal Laboratorio Mobilità e Trasporti del Politecnico di Milano in qualità di Centro di Competenza per la Gestione e la Sicurezza dei Trasporti per il Dipartimento di Protezione Civile Nazionale durante l’esercitazione nazionale di Protezione Civile in Valtellina. Le attività svolte, i prodotti realizzati e utilizzati ma soprattutto i risultati e l’esperienza emersi da una esercitazione temporalmente estesa e di estremo rilievo in ambito di Protezione Civile, si ritiene siano ancora estremamente attuali e utili come esempio per la gestione dei trasporti in caso di emergenze rilevanti

Use of oral gadobenate dimeglumine to visualise the oesophagus during magnetic resonance angiography in patients with atrial fibrillation prior to catheter ablation.

BACKGROUND: Atrio-oesophageal fistula was first reported as a fatal complication of surgical endocardial and percutaneous endocardial radiofrequency ablation for atrial fibrillation, with an incidence after catheter ablation between 0.03% and 0.5%. Magnetic resonance angiography (MRA) was usually performed to obtain pre-procedural 3D images, used to merging into an electro-anatomical map, guiding step-by-step ablation strategy of AF. Our aim was to find an easy, safe and cost-effective way to enhance the oesophagus during MRA. METHODS: In 105 consecutive patients, a right-left phase encoding, free breathing, 3D T1 MRA sequence was performed in the axial plane, >24 hours before catheter ablation, using an intravenous injection of gadobenate dimeglumine contrast medium. The oesophagus was enhanced using an oral gel solution of 0.7 mL gadobenate dimeglumine contrast medium mixed with approximately 40 mg thickened water gel, which was swallowed by the patients on the scanning table, immediately before the MRA sequence acquisition. RESULTS: The visualisation of the oesophagus was obtained in 104/105 patients and images were successfully merged, as left atrium and pulmonary veins, into an electro-anatomical map, during percutaneous endocardial radiofrequency ablation. All patients tolerated the study protocol and no immediate or late complication was observed with the oral contrast agent administration. The free-breathing MRA sequence used in our protocol took 7 seconds longer than MRA breath-hold conventional sequence. CONCLUSION: Oesophagus visualization with oral gadobenate dimeglumine is feasible for integration of oesophagus anatomy images into the electro-anatomical map during AF ablation, without undesirable side effects and without significantly increasing cost or examination time

Meta-analysis of risk factors for cutaneous melanoma: I. Common and atypical naevi

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