| Speaker: | Evgeny Shinder (U of Sheffield) |
|---|---|
| Title: | Canonical semiorthogonal decompositions for G-surfaces |
| Date (JST): | Wed, May 20, 2026, 13:30 - 15:00 |
| Place: | Seminar Room B |
| Abstract: |
This is joint work with Alexey Elagin and Julia Schneider. We study semiorthogonal decompositions of derived categories of smooth projective varieties and their behavior under birational transformations. Motivated by Kuznetsov’s conjecture on cubic fourfolds, Kontsevich’s vision of canonical decompositions, and the Noncommutative MMP by Halpern-Leistner we introduce the notion of a G-atomic theory: canonical, mutation-equivalence classes of G-invariant semiorthogonal decompositions compatible with derived contractions with respect to a group G-action. We prove the existence of such a theory in dimension ≤ 2 for any group G, thereby establishing Kontsevich’s conjecture in this case. This framework refines and extends previous work by Auel–Bernardara and yields a complete birational classification of geometrically rational surfaces over perfect fields in terms of their atoms (canonical building blocks of the derived category). These decompositions are analogs of atomic decompositions for quantum cohomology by Katzarkov–Kontsevich–Pantev–Yu. |
