Autoequivalences of toric surfaces

Abstract

We show that the autoequivalence group of the derived category of any smooth projective toric surface is generated by the standard equivalences and spherical twists obtained from -2-curves. In many cases we give all relations between these generators. We also prove a close link between spherical objects and certain pairs of exceptional objects.

12 pages, 6 figures; major changes: statements corrected and strengthened, new section about non-toric examples, to appear in Proc. AMS

References in corpus (3)

• Autoequivalences of derived categories on the minimal resolutions of $A_n$-singularities on surfaces
• Postnikov-Stability versus Semistability of Sheaves
• Derived categories of toric varieties III

Cited by in corpus (2)

• Orthogonally spherical objects and spherical fibrations
• Relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano fibrations