We prove that the signature of Milnor fiber smoothings a $2$-dimensional isolated complete intersection singularity does not exceed negative number determined by geometric genus, embedding dimension and irreducible components exceptional set minimal resolution, which implies Durfee's weak conjecture partial answer to Kerner--N\'emethi's conjecture.

In this paper, we prove that the Stanley–Reisner ideal of any connected simplicial complex of dimension ≥ 2 that is locally complete intersection is a complete intersection ideal. As an application, we show that the Stanley–Reisner ideal whose powers are Buchsbaum is a complete intersection ideal.