Stability conditions on surfaces and contractions of curves

2025/08/09 by Vilches, Nicolás · 1 citation
#14F08 #18G80 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.07019

Abstract

We study Bridgeland stability conditions on smooth surfaces arising from birational morphisms S → T to a singular surface. Assuming that T has only ADE singularities or certain cyclic quotient singularities, we produce pre-stability conditions on S whose central charges depend on the pullback of an ample divisor on T. Moreover, we prove the support property for the cyclic quotient case (including the A_n singularities). These stability conditions arise as limits of the Arcara-Bertram stability conditions on S. In a complementary direction, we study birational maps S → T for which a stability condition S can be obtained using the pullback of an ample class on T. We prove that the morphism cannot contract smooth curves of positive genus.

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