Singularities of moduli of curves with a universal root

In a series of recent papers, Chiodo, Farkas and Ludwig carry out a deep analysis of the singular locus of the moduli space of stable (twisted) curves with an $\ell$-torsion line bundle. They show that for $\ell\leq 6$ and $\ell\neq 5$ pluricanonical forms extend over any desingularization. This allows to compute the Kodaira dimension without desingularizing, as done by Farkas and Ludwig for $\ell=2$, and by Chiodo, Eisenbud, Farkas and Schreyer for $\ell=3$. Here we treat roots of line bundles on the universal curve systematically: we consider the moduli space of curves $C$ with a line bundle $L$ such that $L^{\otimes\ell}\cong\omega_C^{\otimes k}$. New loci of canonical and non-canonical singularities appear for any $k\not\in\ell\mathbb{Z}$ and $\ell>2$, we provide a set of combinatorial tools allowing us to completely describe the singular locus in terms of dual graph. We characterize the locus of non-canonical singularities, and for small values of $\ell$ we give an explicit description.Comment: 30 pages, to appear in Documenta Mathematic

Moduli of GG-covers of curves: geometry and singularities

In a recent paper Chiodo and Farkas described the singular locus and the locus of non-canonical singularities of the moduli space of level curves. In this work we generalize their results to the moduli space $\overline{\mathcal R}_{g,G}$ of curves with a $G$-cover for any finite group $G$. We show that non-canonical singularities are of two types: $T$-curves, that is singularities lifted from the moduli space $\overline{\mathcal M}_g$ of stable curves, and $J$-curves, that is new singularities entirely characterized by the dual graph of the cover. Finally, we prove that in the case $G=S_3$, the $J$-locus is empty, which is the first fundamental step in evaluating the Kodaira dimension of $\overline{\mathcal R}_{g,S_3}$.Comment: 35 pages. arXiv admin note: text overlap with arXiv:1504.0056

Birational geometry of moduli of curves with an S3S_3-cover

We consider the space $\mathcal R_{g,S_3}^{S_3}$ of curves with a connected $S_3$-cover, proving that for any odd genus $g\geq 13$ this moduli is of general type. Furthermore we develop a set of tools that are essential in approaching the case of $G$-covers for any finite group $G$.Comment: 32 pages, 1 figur

Environment and Economic Growth: Is Technical Change the Key to Decoupling?

The relationship between economic growth and pollution is very complex, depending upon a host of different factors. Thus the study of this phenomenon represents a challenging endeavor. While most economics papers begin with theory and support that theory with econometric evidence, the literature on Environmental Kuznets Curves has proceeded in the opposite direction: first developing an empirical observation about the world, and then attempting to supply appropriate theories. A number of papers have aimed at providing the theoretical underpinnings to the Environmental Kuznets Curve. Prominent here is the class of optimal growth models. These are usually studied from the point of view of the analytical conditions that must hold in order to obtain an inverted-U functional relationship between pollution and growth. These models are however seldom confronted with the data. In this paper we take one popular optimal growth model designed for climate change policy analysis and carry out a few simulation exercises with the purpose of characterizing the relationship between economic growth and emissions. In particular, we try to assess the relative contribution of the ingredients of the well-known decomposition of the environment-growth relationship put forth by Grossman (1995): according to it, the presumed inverted-U pattern results from the joint effect of scale, composition, and technology components. We do this focusing on the developed regions of the world and on a global pollutant, CO2 emissions.Climate Policy, Environmental Modeling, Integrated Assessment, Technical Change

Do Domestic Firms Benefit from Geographical Proximity with Foreign Investors? Evidence from the Privatization of the Czech Glass Industry

This paper analyzes the effects of geographical proximity and agglomeration of foreign direct investors on domestic firms in the privatized glass sector in the Czech Republic. The motivation for this research is based on the scant evidence in Central and Eastern Europe of the effects of geographical proximity and agglomeration on the productivity of domestic firms. This study aims to explain how spillovers are transferred from foreign direct investors to domestic firms in an industrial sector. The econometrical analysis, using original panel data from 1990 to 2006, provides evidence that the geographical proximity to foreign direct investors has a negative and significant effect on the productivity of domestic firms in the glass sector. The effect of agglomeration of foreign direct investors is significant, too. The results support the importance of geographic proximity and the agglomeration of foreign direct investors as a channel of spillovers and it conforms with the evidence that shows that fore ign direct investors have produced negative spillovers on domestic firms in transition countries. The analysis shows, however, that spillovers do not play a dominant role for the performance of privatized domestic firms in the glass sector and the importance of taking into account the industrial sector in the study of spillovers.FDI, agglomeration economies, panel data, regional location, glass industry

Towards computable analysis on the generalised real line

In this paper we use infinitary Turing machines with tapes of length $\kappa$ and which run for time $\kappa$ as presented, e.g., by Koepke \& Seyfferth, to generalise the notion of type two computability to $2^{\kappa}$, where $\kappa$ is an uncountable cardinal with $\kappa^{<\kappa}=\kappa$. Then we start the study of the computational properties of $\mathbb{R}_\kappa$, a real closed field extension of $\mathbb{R}$ of cardinality $2^{\kappa}$, defined by the first author using surreal numbers and proposed as the candidate for generalising real analysis. In particular we introduce representations of $\mathbb{R}_\kappa$ under which the field operations are computable. Finally we show that this framework is suitable for generalising the classical Weihrauch hierarchy. In particular we start the study of the computational strength of the generalised version of the Intermediate Value Theorem

Economic Development and Environmental Protection

There is a long-standing debate on the relationship between economic development and environmental quality. From a sustainable development viewpoint there has been a growing concern that the economic expansion of the world economy will cause irreparable damage to our planet. In the last few years several studies have appeared dealing with the relationship between the scale of economic activity and the level of pollution. In particular, if we concentrate on local pollutants several empirical studies have identified a bell shaped curve linking pollution to per capita GDP (in the case of global pollutants like CO2 the evidence is less clear-cut). This behaviour implies that, starting from low per capita income levels, per capita emissions or concentrations tend to increase but at a slower pace. After a certain level of income (which typically differs across pollutants) – the “turning point” – pollution starts to decline as income further increases. In analogy with the historic relationship between income distribution and income growth, the inverted-U relationship between per capita income and pollution has been termed “Environmental Kuznets Curve”. The purpose of this chapter is not to provide an overview the literature: there are several survey papers around doing precisely that. We instead reconsider the explanations that have been put forth for its inverted-U pattern. We look at the literature from this perspective. In addition, without resorting to any econometric estimation, we consider whether simple data analysis can help to shed some light on the motives that can rationalize the Environmental Kuznets Curve.Climate Policy, Environmental Modeling, Integrated Assessment, Technical Change

Moduli spaces of abstract and embedded Kummer varieties

In this paper, we investigate the construction of two moduli stacks of Kummer varieties. The first one is the stack $\mathcal K^{\text{abs}}_g$ of abstract Kummer varieties and the second one is the stack $\mathcal K^{\text{em}}_g$ of embedded Kummer varieties. We will prove that $\mathcal K^{\text{abs}}_g$ is a Deligne-Mumford stack and its coarse moduli space is isomorphic to $\boldsymbol A_g$, the coarse moduli space of principally polarized abelian varieties of dimension $g$. On the other hand we give a modular family $\mathcal W_g\to U$ of embedded Kummer varieties embedded in $\mathbb P^{2^g-1}\times\mathbb P^{2^g-1}$, meaning that every geometric fiber of this family is an embedded Kummer variety and every isomorphic class of such varieties appears at least once as the class of a fiber. As a consequence, we construct the coarse moduli space $\boldsymbol{\mathsf K}^{\text{em}}_2$ of embedded Kummer surfaces and prove that it is obtained from $\boldsymbol A_2$ by contracting a particular curve inside this space. We conjecture that this is a general fact: $\boldsymbol{\mathsf K}^{\text{em}}_g$ could be obtained from $\boldsymbol A_g$ via a contraction for all $g>1$.Comment: 31 page

Evidence for vertical motility in Campanian deep-water agglutinated foraminifera: The Furlo volcanic ash layer

Evidence for vertical motility has been observed among six Campanian deep-water agglutinated foraminiferal species from the Furlo Bentonite in the Umbria-Marche Basin, Ital