TL;DR
This paper explores properties of multinets in complex projective planes, focusing on inducibility and completeness, and classifies complete 3-nets with implications for hyperplane arrangements and cohomology.
Contribution
It introduces and analyzes the properties of inducibility and completeness in multinets, providing a classification of complete 3-nets and exploring their relationships.
Findings
Classification of complete 3-nets.
Examples illustrating inducibility and completeness.
Insights into multinets' role in hyperplane arrangements.
Abstract
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane . They appear in the study of resonance and characteristic varieties of complex hyperplane arrangement complements and cohomology of Milnor fibers. In this paper, two properties of multinets, inducibility and completeness, and the relationship between them are explored with several examples presented. Specializations of multinets plays an integral role in our findings. The main result is the classification of complete 3-nets.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models