Moduli Spaces of Arrangements of 10 Projective Lines with Quadruple Points

We classify moduli spaces of arrangements of 10 lines with quadruple points. We show that moduli spaces of arrangements of 10 lines with quadruple points may consist of more than 2 disconnected components, namely 3 or 4 distinct points. We also present defining equations to those arrangements whose moduli spaces are still reducible after taking quotients of complex conjugations.Comment: Changed notations in the definition of moduli space to improve clarity. Results unchange

Erratum to “Fundamental groups of some special quadric arrangements”

This erratum relates to our work “Fundamental groups of some special quadric arrangements”. The original Theorems 2.2, 2.5, 2.8 and Propositions 2.3(ii)(iii), 2.6(ii)(iii), 2.9(ii)(iii) have wrong results. They need to be rephrased. Corollaries 2.4 and 2.7 are incomplete, and they are extended. We add a new Corollary 2.10, which does not appear in the original paper. Proposition 3.1 has a wrong result and it is rephrased and reproved. In Proposition 4.1 and its Corollary 4.2 a slight error has occurred: as the correct proofs in the paper show, the monodromy is a quadruple fulltwist.This erratum relates to our work “Fundamental groups of some special quadric arrangements”. The original Theorems 2.2, 2.5, 2.8 and Propositions 2.3(ii)(iii), 2.6(ii)(iii), 2.9(ii)(iii) have wrong results. They need to be rephrased. Corollaries 2.4 and 2.7 are incomplete, and they are extended. We add a new Corollary 2.10, which does not appear in the original paper. Proposition 3.1 has a wrong result and it is rephrased and reproved. In Proposition 4.1 and its Corollary 4.2 a slight error has occurred: as the correct proofs in the paper show, the monodromy is a quadruple fulltwist