On the unipotence of autoequivalences of toric complete intersection Calabi-Yau categories

We identify a class of autoequivalences of triangulated categories of singularities associated with Calabi-Yau complete intersections in toric varieties. Elements of this class satisfy relations that are directly linked to the toric data.

💡 Research Summary

The paper investigates a new class of autoequivalences of the triangulated categories of singularities associated with Calabi‑Yau complete intersections in toric varieties. After recalling the construction of the derived category of singularities (D_{\mathrm{sg}}(Y)) for a Calabi‑Yau complete intersection (Y) defined as the zero‑locus of a generic anticanonical section in a toric variety (X_\Sigma), the authors introduce two elementary operations on this category: (i) tensoring with the line bundles (\mathcal{O}_X(D_i)) corresponding to the toric divisors (D_i) (the “multiplicative” autoequivalences (M_i)), and (ii) the shift functor (