Local syzygies of multiplier ideals

In recent years, multiplier ideals have found many applications in local and global algebraic geometry. Because of their importance, there has been some interest in the question of which ideals on a smooth complex variety can be realized as multiplier ideals. Other than integral closure no local obstructions have been known up to now, and in dimension two it was established by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is locally a multiplier ideal. We prove the somewhat unexpected result that multiplier ideals in fact satisfy some rather strong algebraic properties involving higher syzygies. It follows that in dimensions three and higher, multiplier ideals are very special among all integrally closed ideals.Comment: 8 page

Algebraic varieties with automorphism groups of maximal rank

We confirm, to some extent, the belief that a projective variety X has the largest number (relative to the dimension of X) of independent commuting automorphisms of positive entropy only when X is birational to a complex torus or a quotient of a torus. We also include an addendum to an early paper though it is not used in the present paper.Comment: Mathematische Annalen (to appear

On the canonical map of surfaces with q>=6

We carry out an analysis of the canonical system of a minimal complex surface of general type with irregularity q>0. Using this analysis we are able to sharpen in the case q>0 the well known Castelnuovo inequality K^2>=3p_g+q-7. Then we turn to the study of surfaces with p_g=2q-3 and no fibration onto a curve of genus >1. We prove that for q>=6 the canonical map is birational. Combining this result with the analysis of the canonical system, we also prove the inequality: K^2>=7\chi+2. This improves an earlier result of the first and second author [M.Mendes Lopes and R.Pardini, On surfaces with p_g=2q-3, Adv. in Geom. 10 (3) (2010), 549-555].Comment: Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in the special issue of Science of China Ser.A: Mathematics dedicated to him. V2:some typos have been correcte

Characterization of the 4-canonical birationality of algebraic threefolds

In this article we present a 3-dimensional analogue of a well-known theorem of E. Bombieri (in 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let $X$ be a projective minimal 3-fold of general type with $\mathbb{Q}$-factorial terminal singularities and the geometric genus $p_g(X)\ge 5$. We show that the 4-canonical map $\phi_4$ is {\it not} birational onto its image if and only if $X$ is birationally fibred by a family $\mathscr{C}$ of irreducible curves of geometric genus 2 with $K_X\cdot C_0=1$ where $C_0$ is a general irreducible member in $\mathscr{C}$.Comment: 25 pages, to appear in Mathematische Zeitschrif

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co

The classification of isotrivially fibred surfaces with p_g=q=2

An isotrivially fibred surface is a smooth projective surface endowed with a morphism onto a curve such that all the smooth fibres are isomorphic to each other. The first goal of this paper is to classify the isotrivially fibred surfaces with $p_g=q=2$ completing and extending a result of Zucconi. As an important byproduct, we provide new examples of minimal surfaces of general type with $p_g=q=2$ and $K^2=4,5$ and a first example with $K^2=6$.Comment: Main paper by M.Penegini. Appendix by S.Rollenske. 31 pages, 6 Figures. v2 changed group relations in Theorem 5.2, changes in Theorem 5.7, new proof of Theorem 4.15, minor corrections of misprint

Micronucleus frequency in children exposed to biomass burning in the Brazilian Legal Amazon region: a control case study

<p>Abstract</p> <p>Background</p> <p>The Amazon represents an area of 61% of Brazilian territory and is undergoing major changes resulting from disorderly economic development, especially the advance of agribusiness. Composition of the atmosphere is controlled by several natural and anthropogenic processes, and emission from biomass burning is one with the major impact on human health. The aim of this study was to evaluate genotoxic potential of air pollutants generated by biomass burning through micronucleus assay in exfoliated buccal cells of schoolchildren in the Brazilian Amazon region.</p> <p>Methods</p> <p>The study was conducted during the dry seasons in two regions of the Brazilian Amazon. The assay was carried out on buccal epithelial cells of 574 schoolchildren between 6-16 years old.</p> <p>Results</p> <p>The results show a significant difference between micronucleus frequencies in children exposed to biomass burning compared to those in a control area.</p> <p>Conclusions</p> <p>The present study demonstrated that in situ biomonitoring using a sensitive and low cost assay (buccal micronucleus assay) may be an important tool for monitoring air quality in remote regions. It is difficult to attribute the increase in micronuclei frequency observed in our study to any specific toxic element integrated in the particulate matters. However, the contribution of the present study lies in the evidence that increased exposure to fine particulate matter generates an increased micronuclei frequency in oral epithelial cells of schoolchildren.</p