2013/04/08 by Giuliana Fatabbi, Fatabbi, Giuliana, Brian Harbourne +3
Computer Science · Mathematics · #13A02 #13F20 #14C20 #14N05 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1304.2217
openalex publication_date 2013/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces complexes of linear varieties, called inclics (for INductively Constructible LInear ComplexeS). As examples, we study galaxies (these are constructed starting with a star configuration to which we add general points in a larger projective space). By assigning an order of vanishing (i.e., a multiplicity) to each member of the complex, we obtain fat linear varieties (fat points if all of the linear varieties are points). The scheme theoretic union of these fat linear varieties gives an inclic scheme X. For such a scheme, we show there is an inductive procedure for computing the Hilbert function of its defining ideal IX, regardless of the choice of multiplicities. As an application, we show how our results allow the computation of the Hilbert functions of, for example, symbolic powers (IX)(m) for arbitrary m of many new examples of radical ideals (IX), and we explicitly compute the Waldschmidt constants γ(IX) for galactic inclics X.