The need exists to create the auxotrophic mutants for basidiomycete Ustilago maydis to allow selection of gene transformants in minimal growth media. The ADE2 gene was identified by homology with Saccharomyces cerevisiae. Adenine-requiring auxotrophic mutants were effectively created by homologous recombination in protoplasts using a standard plasmid containing the ADE2 locus interrupted by a p...

Let R be a standard graded commutative algebra over field k , let K its Koszul complex viewed as differential -algebra, and H the homology of . This paper studies interplay between homological properties three algebras In particular, we introduce two definitions Koszulness that extend familiar property originally introduced by Priddy: one which applies to (and, more generally, any connected -al...

We consider constraints on the topology of closed 3-manifolds that can arise as hypersurfaces contact type in standard symplectic $R^4$. Using an obstruction derived from Heegaard Floer homology we prove no Brieskorn sphere admits a embedding $R^4$, result has bearing conjectures Gompf and Koll\'ar. This implies particular rationally convex domain $C^2$ boundary diffeomorphic to sphere. also gi...