Superfat points and associated tensors

2023/05/14 by Canino, Stefano, Catalisano, Maria Virginia, Gimigliano, Alessandro +1 · 2 citations
#14C99 #14N07 #15A69 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.08162

Abstract

We consider 0-dimensional schemes supported at a single point in n-space that are m-symmetric, i.e. that intersect any smooth curve passing through the point with length m, and the ones among them that are maximal with respect to inclusion (called m-superfat points). We study properties of such schemes, in particular for n=2. We give a first application of the simplest such schemes, namely 2-superfat points in the plane, by studying varieties defined by them on Veronese and Segre-Veronese varieties and the (symmetric or partially symmetric) tensors they parameterize.

Cited by

• A new bound on the rank of tensor product of W-states
• Postulation of schemes of length at most 4 on surfaces

Related

• Postulation for 2-superfat points in the plane
• Segre's Regularity Bound for Fat Point Schemes
• Algebraic geometry in tensor categories
• The regularity of points in multi-projective spaces
• The role of the cotangent bundle in resolving ideals of fat points in the plane