Smoothable zero dimensional schemes and special projections of algebraic varieties

2018/07/26 by Jelisiejew, Joachim, Kapustka, Grzegorz, Kapustka, Michal
#14C05 (primary) #14E07 #14J10 (secondary) #14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.10373

Abstract

We study the degrees of generators of the ideal of a projected Veronese variety v₂(ℙ³)⊂ ℙ⁹ to ℙ⁶ depending on the center of projection. This is related to the geometry of zero dimensional schemes of length 8 in \mathbbA⁴, Cremona transforms of ℙ⁶, and the geometry of Tonoli Calabi-Yau threefolds of degree 17 in ℙ⁶.

Related

• VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on A⁶
• Sumsets and Veronese varieties
• Chordal varieties of Veronese varieties and catalecticant matrices
• Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes
• Tangential varieties of Segre-Veronese varieties