Communications in Analysis and Geometry

Volume 19 (2011)

Number 5

New invariants for complex manifolds and isolated singularities

Pages: 991 – 1021



Rong Du (Department of Mathematics, East China Normal University, Shanghai, China)

Hing Sun Luk (Department of Mathematics, The Chinese University of Hong Kong)

Stephen Yau (Department of Mathematical Sciences, Tsinghua University, Beijing, China)


In this paper, we introduce some new invariants for complexmanifolds. These invariants measure in some sense how far thecomplex manifolds are away from having global complex coordinates.For applications, we introduce two new invariants $f^{(1,1)}$ and$g^{(1,1)}$ for isolated surface singularities. We show that$f^{(1,1)}=g^{(1,1)}=1$ for rational double points and cyclicquotient singularities.

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