Zhang, John Min

This dissertation investigates objects known as ``shifted-localized derivators'' through the lens of algebraic geometry by building affine and projective space objects over an arbitrary derivator. For affine space, we give a definition of $\bbA^n$ over a derivator $\bbD$, and then show a series of results identifying it as extending the $\bbA^n$-co...

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, Sławomir Sarti, Alessandra Szemberg, Tomasz
Published in
Jahresbericht der Deutschen Mathematiker-Vereinigung

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

Mboro, René
Published in
manuscripta mathematica

We adapt for algebraically closed fields k of characteristic >2 two results of Voisin (On the universal CH0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {CH} _0...

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...