On Gorenstein Surfaces Dominated by P^2

In this paper we prove that a normal Gorenstein surface dominated by the projective plane P^2 is isomorphic to a quotient P^2/G, where G is a finite group of automorphisms of P^2 (except possibly for one surface V_8'). We can completely classify all such quotients. Some natural conjectures when the surface is not Gorenstein are also stated.Comment: Nagoya Mathematical Journal, to appea

On the Zariski-Lipman conjecture for normal algebraic surfaces

We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several classes of affine and projective surfaces.Comment: Final version; to appear in Jour. London Math. So

Population density controls on microbial pollution across the Ganga catchment

For millions of people worldwide, sewage-polluted surface waters threaten water security, food security and human health. Yet the extent of the problem and its causes are poorly understood. Given rapid widespread global urbanisation, the impact of urban versus rural populations is particularly important but unknown. Exploiting previously unpublished archival data for the Ganga (Ganges) catchment, we find a strong non-linear relationship between upstream population density and microbial pollution, and predict that these river systems would fail faecal coliform standards for irrigation waters available to 79% of the catchment’s 500 million inhabitants. Overall, this work shows that microbial pollution is conditioned by the continental-scale network structure of rivers, compounded by the location of cities whose growing populations contribute c. 100 times more microbial pollutants per capita than their rural counterparts