On Multi-Index Filtrations Associated to Weierstraß Semigroups

This paper is a survey on the main techniques involved in the computation of the Weierstraß semigroup at several points of curves defined over perfect fields, with special emphasis on the case of two points. Some hints about the usage of some packages of the computer algebra software Singular are also given; these are however only valid for curves defined over Fp with p a prime number

The Genome of Botrytis cinerea, a Ubiquitous Broad Host Range Necrotroph

Botrytis cinerea is a necrotrophic ascomycete, causing serious pre- and postharvest crop losses worldwide on a wide variety of plant species. Considerable research in recent years has unraveled a variety of molecular tools that enables the fungus to invade host tissue, including the secretion of toxic proteins and metabolites and host cell wall degrading enzymes. High-quality sequences from two strains of B. cinerea revealed an average-sized genome with a low fraction of repetitive DNA and no specific features correlated with its pathogenic lifestyle, except for a large number of genes encoding pectin-degrading enzymes that are particularly active on cell walls of dicot hosts. The genome sequences enabled genomics, transcriptomics, proteomics, and map-based cloning approaches that have resulted in the identification of genes important for the regulation of secondary metabolite synthesis, drug efflux, light-dependent processes, and pathogenicity. The recent availability of more genome sequences from different B. cinerea strains and Botrytis species and the combination of different ‘omics’ approaches will rapidly increase our understanding of the biology and diverse infection strategies of the gray mold fungus