Semiorthogonal decomposition of $\mathrm{D}^b(\mathrm{Bun}_2^L)$

Abstract

We study the derived category of coherent sheaves on various versions of moduli space of vector bundles on curves by the Borel-Weil-Bott theory for loop groups and Θ-stratification, and construct a semiorthogonal decomposition with blocks given by symmetric powers of the curve.

Derived Category and ACM Bundles of Moduli Space of Vector Bundles on a Curve

“…Toward the proof of Conjecture 1.2, Lee and Narasimhan showed that by analyzing the Hecke correspondence, D 𝑏 (𝑋 2 ) is embedded [LN21] when X is nonhyperelliptic and 𝑔 ≥ 16. After this, Tevelev-Torres and Xu-Yau showed that the above building blocks are embedded in D 𝑏 (M(2, 𝐿)) with entirely different approaches [TT21,XY21]. After an early draft of this paper was circulated, very recently, the remaining generation part was proved by Tevelev [Tev23].…”