Deformations of algebraic schemes via Reedy-Palamodov cofibrant resolutions

Let $X$ be a Noetherian separated and finite dimensional scheme over a field $\mathbb{K}$ of characteristic zero. The goal of this paper is to study deformations of $X$ over a differential graded local Artin $\mathbb{K}$-algebra by using local Tate-Quillen resolutions, i.e., the algebraic analog of the Palamodov's resolvent of a complex space. The above goal is achieved by describing the DG-Lie algebra controlling deformation theory of a diagram of differential graded commutative algebras, indexed by a direct Reedy category.Comment: Final version. To appear in Indagationes Mathematica

Model categories in deformation theory

The aim is the formalization of Deformation Theory in an abstract model category, in order to study several geometric deformation problems from a unified point of view. The main geometric application is the description of the DG-Lie algebra controlling infinitesimal deformations of a separated scheme over a field of characteristic 0

Formal deformation theory in left-proper model categories

We develop the notion of deformation of a morphism in a left-proper model category. As an application we provide a geometric/homotopic description of deformations of commutative (non-positively) graded differential algebras over a local DG-Artin ring

Hyper-holomorphic connections on vector bundles on hyper-K\"ahler manifolds

We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles on hyper-K\"ahler manifolds of arbitrary dimension. We describe the DG Lie algebra controlling this deformation problem, and prove that it is formal when the connection is hyper-holomorphic. Moreover, we prove associative formality for derived endomorphisms of a holomorphic vector bundle admitting a projectively hyper-holomorphic connection.Comment: 26 pages. Comments are very welcome

Formality conjecture for minimal surfaces of Kodaira dimension 0

Let be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the differential graded (DG) Lie algebra of derived endomorphisms of is formal. The proof is based on the study of equivariant minimal models of DG Lie algebras equipped with a cyclic structure of degree 2 which is non-degenerate in cohomology, and does not rely (even for K3 surfaces) on previous results on the same subject

Formality conjecture for minimal surfaces of Kodaira dimension 0

Let F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the DG-Lie algebra RHom(F,F) of derived endomorphisms of F is formal. The proof is based on the study of equivariant $L_{\infty}$ minimal models of DG-Lie algebras equipped with a cyclic structure of degree 2 which is non-degenerate in cohomology, and does not rely (even for K3 surfaces) on previous results on the same subject.Comment: Post-print version; accepted for publication in Compositio Mathematic

Targeted β-Phase Formation in Poly(fluorene)-Ureasil Grafted Organic-Inorganic Hybrids

© 2017 American Chemical Society. The development of synthetic strategies to control the molecular organization (and inherently linked optoelectronic properties) of conjugated polymers is critical for the development of efficient light-emitting devices. Here, we report a facile route using sol-gel chemistry to promote the formation of the β-phase through the covalent-grafting of poly[(9,9-dioctylfluorene)-co-(9,9-bis(8-hydroxyoctyl)fluorene)] (PFO-OH) to poly(oxyalkylene)/siloxane hybrids known as ureasils, due to the urea linkages binding the organic and inorganic components. Although grafting occurs within the siliceous domains, the degree of branching of the organic backbone determines the packing of the PFO-OH chains within the ureasil framework. Moreover, photoluminescence studies indicate that physical confinement also plays a key role in promoting the evolution of the β-phase of PFO-OH as the sol-gel transition proceeds. Spectroscopic and structural analyses reveal that dibranched ureasils promote linear packing of the PFO-OH chains, while tribranched ureasils exhibit a more open, distorted structure that restricts the packing efficacy and reduces the number of covalent anchorages. These results indicate that the organic-inorganic hybrid structure induces distinct levels of β-phase formation and that covalent grafting is a versatile approach to design novel poly(fluorene) hybrid materials with tailored optical properties

Integration of Renewable Energy Systems at City Gate Stations to Reduce Pre-Heating Gas Consumption

The Italian Natural Gas (NG) distribution network includes thousands of NG metering and pressure reduction stations, called City Gate Stations (CGS), for injecting gas into low-pressure networks. These plants are mainly based on the isenthalpic throttling of the gas flow to reduce its pressure, which leads to a significant reduction of its temperature by the Joule-Thompson effect. Gas preheating systems that avoid excessive cooling are installed upstream of pressure reduction valves and usually exploit conventional gas boilers. The energy consumption and carbon footprint could be reduced by integrating heat pumps coupled with renewable energy sources for NG preheating to support gas boilers. For this work, an ad-hoc thermodynamic model for estimating the thermal energy demand for pre-heating is developed, exploiting experimental data from a real CGS, and simplified models of heat pumps and renewable systems. This work aims to assess the actual technical and economic feasibility of energy savings through these technologies. Results show the validated model to be sufficiently accurate to estimate the need for gas preheating for these applications. For the considered case study, up to 38%, 32%, or 26% of the total thermal energy can be recovered with a PBT of less than 20 years, 15, and about 13 years, respectively