Autoequivalences and stability conditions on a degenerate K3 surface

2025/10/15 by H. ARAI, Arai, Hayato
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2510.13526

Abstract

We study autoequivalences and stability conditions on the derived category of coherent sheaves on a singular surface X which arises as an open subvariety of a type III Kulikov degeneration of K3 surfaces. The surface X consists of four irreducible components, one of which is ℙ², and the others are non-compact rational surfaces. Using a comparison with the total space of the degeneration, we show that the connected component Stab^†(D^b_ℙ²(X)) of the space of stability conditions on the supported derived category D^b_ℙ²(X) containing geometric stability conditions is simply connected, and describe its wall-and-chamber structure via half-spherical twists. As consequences, we determine the subgroup of the autoequivalence group Aut(D^b(X)) that preserves this component; it is isomorphic to ℤ × Γ₁(3) × Aut(X), where Γ₁(3) ⊂ SL(2,ℤ) is the congruence subgroup of level~3.

Citations

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Related

• Central derived autoequivalences of K3 surfaces
• Stability conditions on K3 surfaces
• Spherical twists, relations and the center of autoequivalence groups of K3 surfaces
• Half-spherical twists on derived categories of coherent sheaves
• Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations