The direct image of the relative dualizing sheaf needs not be semiample

We provide details for the proof of Fujita's second theorem and prove that for a Kähler fibre space f:X→B$f:X\to B$ over a smooth projective curve B  , the direct image of the relative dualizing sheaf V:=f_?ω_X/B$V:=f_{?}{\omega }_{X/B}$ is the direct sum of an ample and a unitary flat bundle. We also show that V needs not be semiample, which is our main result.     

Overconvergent modular sheaves and modular forms for GL 2/F

Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ?, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.     

A Cauchy kernel for slice regular functions

In this article, we show how to construct a regular, non-commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results.     

Secondary ion mass spectrometric investigation of Au-based composites.

The electrodeposition of thick gold layers plays an important role both in traditional and high-tech productions, such as jewelry and microelectronics, respectively. In this work a secondary ion mass spectrometric study will be presented on Au co-deposits with (sub-)micrometric ceramic powders, in order to harden gold. Mass spectra are used to identify the components deposited, providing evidence of the additives and/or eventual contaminants introduced during electrolysis. Furthermore, analysis of ion depth profiles and the intensity distribution of ionic species along the film were studied.     

Functional rearrangement of 3-Cl or 3,3-diCl-γ-lactams bearing a secondary 1-chloroalkyl substituent at C-4

The study of the reaction with MeONa/MeOH of chlorinated γ-lactams, prepared from the atom transfer radical cyclization of N-allyl-α-perchloroamides, has been extended to the case of substrates carrying an exo halogen atom on a branched carbon. Only with secondary exo C-Cl groups, that are not located on a fused ring, does the functional rearrangement follow the typical transformation route, which with trichloro-lactams can proceed further to give 4-alkylidene derivatives. From a practical point of view, the outcome of the reaction with di- or trichloro N-cinnamylamides is synthetically valuable, affording the 5-methoxy-1H-pyrrol-2(5H)-one or 3-benzylidenepyrrolidine-2,5-dione, respectively, in good to excellent yield.