Reduced and non-reduced linear spaces: Lines and points

2013/08/30 by Enrico Carlini, Carlini, Enrico, Maria Virginia Catalisano +3
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1308.6796

arXiv admin note: substantial text overlap with arXiv:1006.2290

arxiv created 2013/08/30 · openalex publication_date 2013/08/30 · arxiv updated 2013/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the problem of determining the Hilbert function of schemes X of the proiective space Pⁿ which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n > 3. When n=3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.

Citations

• 3-dimensional sundials

Related

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• Postulation of generic lines and one double line in \PPⁿ in view of generic lines and one multiple linear space
• Hilbert schemes of points and applications
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• The Relevant Domain of the Hilbert Function of a Finite Multiprojective Scheme