On compactifications of Mg,n\mathcal{M}_{g,n} with colliding markings

In this paper, we study all ways of constructing modular compactifications of the moduli space $\mathcal{M}_{g,n}$ of $n$-pointed smooth algebraic curves of genus $g$ by allowing markings to collide. We find that for any such compactification, collisions of markings are controlled by a simplicial complex which we call the collision complex. Conversely, we identify modular compactifications of $\mathcal{M}_{g,n}$ with essentially arbitrary collision complexes, including complexes not associated to any space of weighted pointed stable curves. These moduli spaces classify the modular compactifications of $\mathcal{M}_{g,n}$ by nodal curves with smooth markings as well as the modular compactifications of $\mathcal{M}_{1,n}$ with Gorenstein curves and smooth markings. These compactifications generalize previous constructions given by Hassett, Smyth, and Bozlee--Kuo--Neff.Comment: 41 pages; minor corrections since last revision, comments very welcom

A stratification of moduli of arbitrarily singular curves

We construct a stratification $\bigsqcup_\Gamma \mathscr{E}_\Gamma$ of moduli of arbitrarily singular reduced curves indexed by generalized dual graphs and prove that each stratum is a fiber bundle over a finite quotient of a product of $\mathcal{M}_{g,n}$'s. The fibers are locally closed subschemes of products of Ishii's "territories," projective moduli schemes parametrizing subalgebras of a fixed algebra. The setting for our stratification is a new moduli stack $\mathscr{E}_{g,n}$ of "equinormalized curves" which is a minor modification of the moduli space of all reduced, connected curves. We prove algebraicity of substacks $\mathscr{E}^{\delta,\delta'}_{g,n}$ where invariants $\delta, \delta'$ are fixed, coarsely stratifying $\mathscr{E}_{g,n}$, then refine this to the desired stratification $\mathscr{E}_\Gamma$. A key technical ingredient is the introduction of the invariant $\delta'$ which allows us to ensure conductors commute with base change.Comment: Corrected definition 1.7, added section comparing territories with crimping spaces. 37 pages, 4 figures. Comments very welcome

Sourcing limestone masonry for restoration of historic buildings: a spectroscopic study

This study presents a combined Fourier transform (FT) mid-infrared, laser Raman and Commission internationale d’éclairage (CIE) L*a*b*system analysis of quarry-derived impure limestone and fallen masonry from a medieval listed building situated in the south east of England, to ascertain how spectroscopic information can be collectively employed to identify the most exacting possible replacement stone source.Data shows that subtle differences in [Al] and [Fe3+] octahedral and tetrahedral site occupancy in glauconite group clays registered in the mid-infrared [3530 cm−1/3620 cm−1] absorption ratio exerts some influence on L*Cab*hab*values. Increases in L*and Cabare associated with decreasing clay content. Theoverall weakness of correlations between infrared and visible range spectral attributes indicates multiple contributing sources to overall color. Evidence indicates that the degree of laser Raman induced background noise is related to the overall calcite content and that activators of fluorescence at 785 nmexcitation wave length may also contribute to rock color. The results are utilized to define closest matching quarry samples to the fallen masonry

A multi-spectroscopic study for the characterization and definition of production techniques of German ceramic sherds

The aim of this archaeometric study is to recover information regarding technological processes and raw materials used for the production of ceramic sherds coming from five central and Eastern German sites, between Lower Saxony and Saxony states. The ceramic fragments have been investigated by a multi-spectroscopic approach: Fourier transform infrared spectroscopy (FT-IR), micro-Raman spectroscopy and X-ray Fluorescence (XRF) were employed to characterize both ceramic bodies and glazes. Moreover the innovative application of Laser Induced Fluorescence (LIF) on ceramic findings has been proposed and evaluated. Chemical and mineralogical composition, as well as microstructure, of ceramic mixture and glaze are correlated to native material composition and firing temperature, which have become a fundamental features in archaeometric research and play a key role in understanding the provenance of the pottery and its production techniques.The multi-spectroscopic approach applied in this work has enabled the ability to characterize the ceramic sherds and to investigate through non-destructive techniques both ceramic glaze and matrix giving information regarding the raw materials and pigments/colourants used, and regarding firing temperature and technology. The present study carried on using complementary methods suggests different raw material sources and temperature kilns. These data are in agreement with the location of ceramic sites and with data in literature. Furthermore, the interesting results suggest that non-destructive techniques, such as LIF and Raman spectroscopy, are promising methods for ceramic and glaze characterization. (C) 2015 Elsevier B.V. All rights reserved

Hyperelliptic Gorenstein curves and logarithmic differentials

We produce a flexible tool for contracting subcurves of logarithmic hyperelliptic curves, which is local around the subcurve and commutes with arbitrary base-change. As an application, we prove that hyperelliptic multiscale differentials determine a sequence of Gorenstein contractions of the underlying nodal curve, whose dualising bundle they descend to generate. This is the first piece of evidence for a more general conjecture about limits of differentials.Comment: 25 pages, 7 figures, comments welcome at all time