Birational automorphism groups of projective varieties of Picard number two

We slightly extend a result of Oguiso on birational or automorphism groups (resp. of Lazi\'c - Peternell on Morrison-Kawamata cone conjecture) from Calabi-Yau manifolds of Picard number two to arbitrary singular varieties X (resp. to klt Calabi-Yau pairs in broad sense) of Picard number two. When X has only klt singularities and is not a complex torus, we show that either Aut(X) is almost cyclic, or it has only finitely many connected components.Comment: title slightly changed to this; some proof simplified; submitted to the Proceedings of Groups of Automorphisms in Birational and Affine Geometry, 28 October - 3 November 2012, C.I.R.M., Trento, Ital

Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in Inventiones Mathematica

Curve classes on irreducible holomorphic symplectic varieties

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.Comment: 15 page

Seismicity and Focal Mechanisms at the Calabro-Lucanian boundary along the Apennine chain (southern Italy)

The Calabro-Lucanian boundary is a complex geological zone marking the transition between the highly seismogenic tectonic domains of Southern Apennines and the Calabrian Arc. Historical catalogues include earthquakes with macroseismic effects up to VII-VIII MCS (CPTI WORKING GROUP, 2004) and paleoseismological investigations suggested that earthquakes of magnitude between 6.5 and 7 may have occurred in this area, between the 6th and the 15th century (MICHETTI et alii, 2000). More recently, on 9 September 1998, an earthquake of moment magnitude M5.6 occurred at the north-western margin of the Pollino massif (GUERRA et alii, 2005; ARRIGO et alii, 2006) and since the second half of 2010 the same region was interested by a noteworthy seismic activity characterized by several swarms with thousands of events with a maximum magnitude of 3.6

Micromechanical Analysis of Soft Tactile Sensors

NP is supported by the European Research Council PoC 2015 “Silkene” No. 693670 and by the European Commission H2020 under the Graphene Flagship Core 1 No. 696656 (WP14 “Polymer Nanocomposites”) and under the FET Proactive “Neurofibres” No. 732344

Evaluation of microbial adhesion and biofilm formation on nano-structured and nano-coated ortho-prosthetic materials by a dynamic model

The bio-engineering technologies of medical devices through nano-structuring and coating was recently proposed to improve biocompatibility and to reduce microbial adhesion in the prevention of implantable device-related infections. Our aim was to evaluate the ability of new nano-structured and coated materials to prevent the adhesion and biofilm formation, according to the American Standard Test Method ASTM-E2647-13. The materials composition was determined by X-ray Fluorescence and Laser Induced Breakdown Spectroscopy. Silver release was evaluated by Inductively Coupled Plasma Mass Spectrometry analysis. The gene expression levels of the Quorum Sensing Las and Rhl system were evaluated by the ΔΔCt method. The Log bacterial density (Log CFU/cm2) on TiAl6V4 was 4.41 ± 0.76 and 4.63 ± 1.01 on TiAl6V4-AgNPs compared to 2.57 ± 0.70 on CoCr and 2.73 ± 0.61 on CoCr-AgNPs (P < 0.0001, A.N.O.V.A.- one way test). The silver release was found to be equal to 17.8 ± 0.2 μg/L after the batch phase and 1.3 ± 0.1 μg/L during continuous flow. The rhlR gene resulted in a 2.70-fold increased expression in biofilm growth on the silver nanoparticles (AgNPs) coating. In conclusion, CoCr showed a greater ability to reduce microbial adhesion, independently of the AgNPs coating. The silver release resulted in promoting the up-regulation of the Rhl system. Further investigation should be conducted to optimize the effectiveness of the coating

Cohomology of bundles on homological Hopf manifold

We discuss the properties of complex manifolds having rational homology of $S^1 \times S^{2n-1}$ including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known vanishing properties of cohomology of bundles on such manifolds.As an application we consider degeneration of Hodge-deRham spectral sequence in this non Kahler setting.Comment: To appear in Proceedings of 2007 conference on Several complex variables and Complex Geometry. Xiamen. Chin

Assessment, control, and prevention of microbiological and chemical hazards in seasonal swimming pools of the Versilia district (Tuscany, central Italy).

Abstract Although in Europe the quality of swimming pools (SPs) is dictated by regulations, microbiological and chemical hazards are described in the literature. Environmental bacteria or toxic disinfection by-product (DBP) compounds may indeed be recovered in waters even after disinfection. We evaluated the water quality from 26 outdoor seasonal SPs of the Versilia district, according to requirements of Regional Decree 54R/2015. In spring 2017, supply and reinstatement waters were collected after shock hyperchlorination (10 mg/L) while in summertime, a second sampling of waters before entering the pools, as well as in the pools, was performed after SPs were open to the public. In all samples, microbiological and chemical parameters were determined as defined by Directive 98/83/EC and the Italian Health Ministry. Microbiological data were within suggested limits. The first chemical analyses showed that in 35% of the feeding-pool seawater samples, the halogenated organic compounds were higher than the maximum permissible concentrations (30 μg/L). Pool waters were then dechlorinated and re-treated with hydrogen peroxide (10 mg/L) to ensure the abatement of DBPs (from 164 ± 107 to 0.9 ± 0.8 μg/L; p = 0.002). Results highlighted the need of self-controlled procedures for the SPs waters to prevent waterborne diseases and suggested hydrogen peroxide as the most appropriate disinfection method

Cohomological Hasse principle and motivic cohomology for arithmetic schemes

In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.Comment: 47 pages, final versio