A characterization of finite quotients of Abelian varieties

In this paper we prove a characterization of quotients of Abelian varieties by the actions of finite groups that are free in codimension-one via some vanishing conditions on the orbifold Chern classes. The characterization is given among a class of varieties with mild singularities that are more general than quotient singularities, namely among the class of klt varieties. Furthermore we show that over a projective klt variety, any semistable reflexive sheaf with vanishing orbifold Chern classes can be obtained as the invariant part of a locally-free sheaf on a finite Galois cover whose associated vector bundle is flat.Comment: Added more details for the arguments in the final section. To appear in International Mathematics Research Notice

Hyperbolicity of singular spaces

We study the hyperbolicity of singular quotients of bounded symmetric domains. We give effective criteria for such quotients to satisfy Green-Griffiths-Lang's conjectures in both analytic and algebraic settings. As an application, we show that Hilbert modular varieties, except for a few possible exceptions, satisfy all expected conjectures.Comment: Main results extended to arbitrary quotient singularities and all bounded symmetric domain

Organic agriculture: opportunities and challenges

The organic movement may have gained a place in the spotlight of the mainstream media now, but it has not been like that for long. Since the 1950s, organic farmers operating at a grass roots level have devised, tested and shared production methods. They have codified a set of ideals into a pioneering best practice agricultural management system that addresses multiple community values. Niche markets have gradually been created, commonly based on trust and goodwill (formal certification did not begin until the 1960s and 1970s), and often using novel direct marketing strategies such as box schemes and community supported agriculture. After many years of consumers having to hunt around for their organic produce from several suppliers, perhaps directly from the farmer, the task is now a lot easier with specialist food shops and organic shelf space in supermarkets, in the industrialised world at least. Global links have been forged in all continents as organic agriculture has been seen to be an effective rural development option

Nonabelian Hodge Theory for klt spaces and descent theorems for vector bundles

We generalise Simpson's nonabelian Hodge correspondence to the context of projective varieties with klt singularities. The proof relies on a descent theorem for numerically flat vector bundles along birational morphisms. In its simplest form, this theorem asserts that given any klt variety X and any resolution of singularities, then any vector bundle on the resolution that appears to come from X numerically, does indeed come from X. Furthermore and of independent interest, a new restriction theorem for semistable Higgs sheaves defined on the smooth locus of a normal, projective variety is established.Comment: Final version. To appear in Compositio Mathematic

Investigation of management practices and economic viability of vineyards for organic wine production

This paper reports the findings of two components of a research investigating the viability of organic wine grape production. Firstly the results of a survey of Australian organic wine grape growers’ management practices and secondly the first year findings of an experimental organic vineyard compared to an associated conventional vineyard. The survey found a heavy reliance on sulphur and copper sprays for powdery and downy mildew control. The experimental vineyard showed similar yields to conventional growing and in many cases higher sugar, though some increase in botrytis in organic Shiraz

The Miyaoka-Yau inequality and uniformisation of canonical models

We establish the Miyaoka-Yau inequality in terms of orbifold Chern classes for the tangent sheaf of any complex projective variety of general type with klt singularities and nef canonical divisor. In case equality is attained for a variety with at worst terminal singularities, we prove that the associated canonical model is the quotient of the unit ball by a discrete group action.Comment: v3: final version, added section on "Further directions"; accepted for publication by Annales scientifiques de l'Ecole normale sup\'erieur