An Introduction to A1-enumerative geometry

  • Sabrina Pauli (Universität Duisburg-Essen, Essen, Germany)
E1 05 (Leibniz-Saal)


Let $k$ be an arbitrary field and $GW(k)$ its Grothendieck-Witt ring, that is, the group completion of the semi-ring of non-degenerate symmetric bilinear forms over $k$.

New techniques from A1-homotopy theory allow us to count algebro-geometric objects as elements in $GW(k)$. One of the first examples of such enriched counts was the count of lines on a smooth cubic surface by Kass-Wickelgren. The resulting symmetric bilinear form contains information about the count over the chosen base field $k$ and recovers the known classical counts over the complex and real numbers.

In my talk I will explain how to count in $GW(k)$ with the help of some illustrating examples.

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Enis Kaya

University of Groningen

Avinash Kulkarni

Dartmouth College

Antonio Lerario


Mima Stanojkovski

RWTH Aachen and Max Planck Institute for Mathematics in the Sciences