Moduli spaces and related topics in algebraic geometry

Organizers:

Federico Bongiorno, Theodoros Papazachariou

Speaker：

Ruadhai Dervan (University of Warwick)

Time：

Wed., 15:30-16:30, Jan. 14, 2026

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007 Passcode: YMSC

Venue：

Metric wall-crossing

Abstract:

When a reductive group acts on a projective variety, a choice of (linearised) ample line bundle gives a choice of quotient. Wall-crossing (or VGIT) explains how the quotient space changes with the choice of line bundle: the quotients vary birationally, by flips, and only finitely finite birational models can occur.

I will describe a (Kähler) metric version of these results. Each quotient admits a natural choice of Kähler metric, through a symplectic quotient construction. I will prove metric convergence (towards walls), and the existence of metric flips (across walls), when one suitably varies the choice of line bundle determining the quotient. I will use these results to motivate analogous conjectures governing the metric geometry of moduli spaces in wall-crossing problems in algebraic geometry.