报告题目：Heat kernel asymptotics and local index theorem for open complex manifolds with C*-action

报告时间：2024-03-18  16:00-17:00

报 告 人：郑日新 研究员 (中研院数学研究所)

报告地点：理学院东北楼四楼报告厅（404）

Abstract：For a complex manifold Σ with C^∗-action, we define the m-th C^∗ Fourier-Dolbeault cohomology group and consider the m-index on Σ. By applying the method of transversal heat kernel asymptotics, we obtain a local index formula for the m-index. We can reinterpret Kawasaki’s Hirzebruch-Riemann-Roch formula for a compact complex orbifold with an orbifold holomorphic line bundle by our integral formulas over a (smooth) complex manifold and finitely many complex submanifolds arising from singular strata. By considering the trace integral we conclude the nonexistence of smoothing of orbifold singularities as a consequence.