Görtz, Ulrich
Published in
Jahresbericht der Deutschen Mathematiker-Vereinigung

About 50 years ago, Éléments de Géométrie Algébrique (EGA) by A. Grothendieck and J. Dieudonné appeared, an encyclopedic work on the foundations of Grothendieck’s algebraic geometry. We sketch some of the most important concepts developed there, comparing it to the classical language, and mention a few results in algebraic and arithmetic geometry w...

Lowengrub, Daniel

We develop tools for computing invariants of singular varieties and apply them to the classical theory of nodal curves and the complexity analysis of non-convex optimization problems.The first result provides a method for computing the Segre class of a closed embedding X → Y in terms of the Segre classes of X and Y in an ambient space Z. This metho...

Wen, David

One of the main research programs in Algebraic Geometry is the classification of varieties. Towards this goal two methodologies arose, the first is classifying varieties up to isomorphism which leads to the study of moduli spaces and the second is classifying varieties up to birational equivalences which leads to the study of birational geometry. P...

Bauer, Thomas Hulek, Klaus Rams, Slawomir Sarti, Alessandra Szemberg, Tomasz

In this article we describe the life and work of Wolf Barth who died on 30th December 2016. Wolf Barth's contributions to algebraic variety span a wide range of subjects. His achievements range from what is now called the Barth-Lefschetz theorems to his fundamental contributions to the theory of algebraic surfaces and moduli of vector bundles, and ...

Ciliberto, Ciro Mella, Massimiliano Sernesi, Edoardo
Published in
Rendiconti del Circolo Matematico di Palermo Series 2

Mboro, Rene

We adapt for algebraically closed fields k of characteristic greater than 2 two results of Voisin, on the decomposition of the diagonal of a smooth cubic hypersurface X of dimension 3 over ℂ, namely: the equivalence between Chow-theoretic and cohomological decompositions of the diagonal of those hypersurfaces and the fact that the algebraicity (wit...

Spicer, Calum

We develop some foundational results in a higher dimensional foliated Mori theory, andshow how these results can be used to prove a structure theorem for the Kleiman-Mori coneof curves in terms of the numerical properties of $K_{\cal F}$ for rank 2 foliationson threefolds. We also make progresstoward realizing a minimal model program for rank 2 fol...

Spicer, Calum

We develop some foundational results in a higher dimensional foliated Mori theory, andshow how these results can be used to prove a structure theorem for the Kleiman-Mori coneof curves in terms of the numerical properties of $K_{\cal F}$ for rank 2 foliationson threefolds. We also make progresstoward realizing a minimal model program for rank 2 fol...

Spicer, Calum

We develop some foundational results in a higher dimensional foliated Mori theory, andshow how these results can be used to prove a structure theorem for the Kleiman-Mori coneof curves in terms of the numerical properties of $K_{\cal F}$ for rank 2 foliationson threefolds. We also make progresstoward realizing a minimal model program for rank 2 fol...

Spicer, Calum

We develop some foundational results in a higher dimensional foliated Mori theory, andshow how these results can be used to prove a structure theorem for the Kleiman-Mori coneof curves in terms of the numerical properties of $K_{\cal F}$ for rank 2 foliationson threefolds. We also make progresstoward realizing a minimal model program for rank 2 fol...