16 research outputs found

    On a notion of speciality of linear systems in P^n

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    Given a linear system in P^n with assigned multiple general points we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear system, which takes into account the contribution of the linear base locus, and thus to introduce the notion of linear speciality. We investigate such a notion giving sufficient conditions for a linear system to be linearly non-special for arbitrary number of points, and necessary conditions for small numbers of points.Comment: 26 pages. Minor changes, Definition 3.2 slightly extended. Accepted for publication in Transactions of AM

    Weyl cycles on the blow-up of P4\mathbb{P}^4 at eight points

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    We define the Weyl cycles on XsnX^n_s, the blown up projective space Pn\mathbb{P}^n in ss points in general position. In particular, we focus on the Mori Dream spaces X73X^3_7 and X84X^{4}_{8}, where we classify all the Weyl cycles of codimension two. We further introduce the Weyl expected dimension for the space of the global sections of any effective divisor that generalizes the linear expected dimension and the secant expected dimension

    On the Effective Cone of Pn Blown-up at n + 3 Points

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    © 2016 Taylor & Francis.We compute the facets of the effective and movable cones of divisors on the blow-up of ℙn at n + 3 points in general position. Given any linear system of hypersurfaces of ℙn based at n + 3 multiple points in general position, we prove that the secant varieties to the rational normal curve of degree n passing through the points, aswell as their joinswith linear subspaces spanned by some of the points, are cycles of the base locus andwe compute their multiplicity.We conjecture that a linear systemwith n + 3 points is linearly special only if it contains such subvarieties in the base locus and we give a new formula for the expected dimension

    On linear systems of P3 with nine base points

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    © 2015, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.We study special linear systems of surfaces of P3 interpolating nine points in general position having a quadric as fixed component. By performing degenerations in the blown-up space, we interpret the quadric obstruction in terms of linear obstructions for a quasi-homogeneous class. By degeneration, we also prove a Nagata type result for the blown-up projective plane in points that implies a base locus lemma for the quadric. As an application, we establish Laface–Ugaglia Conjecture for linear systems with multiplicities bounded by 8 and for homogeneous linear systems with multiplicity m and degree up to 2 m+ 1

    Duality and polyhedrality of cones for Mori dream spaces

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    Our goal is twofold. On one hand we show that the cones of divisors ample in codimension kk on a Mori dream space are rational polyhedral. On the other hand we study the duality between such cones and the cones of kk-moving curves by means of the Mori chamber decomposition of the former. We give a new proof of the weak duality property (already proved by Payne and Choi) and we exhibit an interesting family of examples for which strong duality holds.Comment: 20 pages, 1 figur

    New genetic loci link adipose and insulin biology to body fat distribution.

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    Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms

    On a notion of speciality of linear systems in P^n

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    Given a linear system in P^n with assigned multiple general points, we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear system, which takes into account the contribution of the linear base locus, and thus to introduce the notion of linear speciality. We investigate such a notion, giving sufficient conditions for a linear system to be linearly non-special for an arbitrary number of points and necessary conditions for a small number of points

    On linear systems of P3 with nine base points

    Get PDF
    We study special linear systems of surfaces of P3 interpolating nine points in general position having a quadric as fixed component. By performing degenerations in the blown-up space, we interpret the quadric obstruction in terms of linear obstructions for a quasi-homogeneous class. By degeneration, we also prove a Nagata type result for the blown-up projective plane in points that implies a base locus lemma for the quadric. As an application, we establish Laface–Ugaglia Conjecture for linear systems with multiplicities bounded by 8 and for homogeneous linear systems with multiplicity m and degree up to 2m+1

    On the effective cone of Pn blown-up at n+3 points

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    We compute the facets of the effective and movable cones of divisors on the blow-up of Pn at n + 3 points in general position. Given any linear system of hypersurfaces of Pn based at n + 3 multiple points in general position, we prove that the secant varieties to the rational normal curve of degree n passing through the points, as well as their joins with linear subspaces spanned by some of the points, are cycles of the base locus and we compute their multiplicity. We conjecture that a linear system with n + 3 points is linearly special only if it contains such subvarieties in the base locus and we give a new formula for the expected dimension
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