Rigidity and Multiplicity of Singularities Associated to Ample Vector Bundles

Explore a 59-minute lecture on the rigidity and multiplicity of singularities associated with ample vector bundles. Delve into the unique irreducible desingularization of isolated singularities given by the Grauert blow down of negative vector bundles. Discover a formula for calculating the multiplicity of isolated singularities resulting from the Grauert blow down of exceptional divisors in complex manifolds. Learn how this formula can be applied to estimate or provide exact calculations for singularities arising from negative vector bundles. Examine the special case involving compact Riemann surfaces and its connection to classical results on Weierstrass points. Gain insights from this collaborative research presented by Fusheng Deng, based on joint work with Yinji Li, Qunhuan Liu, and Xiangyu Zhou.