GIT Compactifications of M_{0,n} and Flips

We use geometric invariant theory (GIT) to construct a large class of compactifications of the moduli space M_{0,n}. These compactifications include many previously known examples, as well as many new ones. As a consequence of our GIT approach, we exhibit explicit flips and divisorial contractions between these spaces.Comment: Final version to appear in Advance

Camptothecin Analogs and Methods of Preparation Thereof

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Camptothecin Analogs and Methods of Preparation Thereof

To read this abstract, please download this patent

Computation of GIT quotients of semisimple groups

We describe three algorithms to determine the stable, semistable, and torus-polystable loci of the GIT quotient of a projective variety by a reductive group. The algorithms are efficient when the group is semisimple. By using an implementation of our algorithms for simple groups, we provide several applications to the moduli theory of algebraic varieties, including the K-moduli of algebraic varieties, the moduli of algebraic curves and the Mukai models of the moduli space of curves for low genus. We also discuss a number of potential improvements and some natural open problems arising from this work.Comment: 32 pages, 3 figures. 1 tabl

Kontinentale spændinger - matematiske modeller leverer ny viden

Indtil nu har geologer antaget, at hævningsfaserne i de sedimentære bassiner var ledsaget af en samtidig øget tektonisk aktivitet ved pladeranden, men nye computersimulationer har nu vist, at bassinerne også hæves, når den tektoniske aktivitet er på retur

Phosphorus dynamics in Vertosols: improving fertilizer management

Phosphorus (P) increasingly constrains crop productivity in Australian Vertosols (Australian Soil Classification, Isbell et al., 2021). However, P behaviour and dynamics in Vertosols are still not well understood especially within complex cropping systems. To complement our knowledge in P dynamics in Vertosols and collect critical information as a baseline for future agricultural model development, nine Vertosols were incubated with various P fertilizer treatments. Phosphorus dynamics were modelled in relation to physical and chemical properties. Results indicate that physical and chemical properties and P dynamics of the Vertosols are highly variable and differ substantially from the other soil types. This suggests that inclusion of selected soil properties to current soil P models could help to improve the understanding of the fate of applied P in Vertosols. This will be critical for future development of sustainable P fertilizer management strategies