Postulation of schemes of length at most 4 on surfaces

2025/11/28 by Ballico, E., Canino, S.
#14N05 #14N10 #14N15 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.22946

Abstract

In this paper we address the postulation problem of zero-dimensional schemes on a surface of length at most 4. We prove some general results and then we focus on the case of P2, P1xP1 and Hirzebruch surfarces. In particular, we prove that except for few well-known exceptions, a general union of schemes of length at most 4 has always good postulation in P2 and in P1xP1.

Citations

• Postulation for 2-superfat points in the plane
• Superfat points and associated tensors
• On the Jacobian Scheme of a plane curve
• Secant varieties of Segre-Veronese embeddings of (P¹)^r
• Osculating Varieties of Veronesean and their higher secant varieties

Related

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• On an analogue of the Markov equation for exceptional collections of length 4
• A smooth surface in P4 not of general type has degree at most 46
• On Konopelchenko's representation for surfaces in 4 dimensions
• A moduli scheme parametrizing blowups of smooth projective surfaces