Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

3rd of December 2024, 14:30-16:00, room D’Antoni

 

 

 

 

 

 

 

Virtual intersection theory on the space of lines in the plane

 

Dhruv Ranganathan

University of Cambridge

 

 

 

 

The moduli space of stable n-pointed rational curves is a fundamental object in algebraic geometry. Many aspects of the space, such as its intersection theory, have been completely understood. The two dimensional analogue, parameterizing KSBA stable configurations of n lines in the plane, is much more mysterious. It has been studied by a number of researchers, including Alexeev, Hacking-Keel-Tevelev, Lafforgue, and others. I will share a new perspective on this space, motivated by logarithmic geometry, and explain how this perspective can be used to endow the space with a virtual fundamental class, and puts it on essentially equal theoretical footing with its more well-studied sibling. I will then explain the combinatorial structure on the boundary, and discuss where we hope to take the story next. Based on ongoing joint work with Abramovich and Pandharipande.

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures