The second pluri-genus of smoothable Gorenstein surface singularities
Let \((X,x)\) be a Gorenstein smoothable singularity with \(p_g(X,x)\geq 1\). It is proved that \[ \delta_2(X,x)=h^1(S)+\mu(X,x)-\tau(X,x)-p_g(X,x)+1\;. \] Here \(\mu(X,x)\) and \(\tau(X,x)\) are the generalized Milnor number and Tjurina number of \((X,x), \delta_2(X,x)\) is the second pluri-genus and \(p_g(X,x)\) the geometric genus. \(f:(M, E)\to (X,x)\) is the minimal good resolution, \(E\) the exceptional divisor, and \(S=(\Omega_M^1(\log E))^\ast\). This is a generalization of the corresponding result of Okuma, for complete intersection isolated surface singularities.
scientific article; zbMATH DE number 5712123