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Seungjae Lee, Symmetric Differentials on Complex Hyperbolic Forms
April 8 @ 11:00 am - 12:00 pm KST
B266, IBS Korea, Republic of
Let Γ be a cocompact torsion-free lattice in the automorphism group of complex unit ball Bn, Aut(Bn). In this talk, we discuss the existence of symmetric differentials on the compact ball quotient Σ = Bn / Γ. Since Σ has a Kähler metric induced by the Bergman metric on the complex unit ball Bn, it has symmetric differentials on SmTΣ* if m is sufficiently large. Unfortunately, finding the smallest degree m which guarantees a symmetric differential on SmTΣ* is difficult in even compact ball quotient cases. Instead of this, I will prove that m ≥ n+2 is a sufficient condition to give a symmetric differential on SmTΣ*. To achieve this goal, I will explain how to induce symmetric differentials by using a recursive formula for ∂-operators and Poincaré series. This is joint work with A. Seo.