1998/10/19 by Atanas Iliev, Kristian Ranestad, Iliev, Atanas +1
Computer Science · Mathematics · #14J (Primary) 14M (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14J #msc:14M
paper · pdf · doi:10.48550/arxiv.math/9810121
15 pages appeared in Trans. Amer. Math. Soc. 353, No.4, 1455-1468 (2001)
openalex publication_date 1998/10/19 · arxiv created 2006/11/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main outcome of this paper is that the variety VSP(F,10) of presentations of a general cubic form F in 6 variables as a sum of 10 cubes is a smooth symplectic 4-fold obtained a deformation of the Hilbert square of a K3 surface of genus 8. After publishing it in Trans. Am. Math. Soc. 353, No.4, 1455-1468 (2001), it was noted to us by Eyal Markman that in Theorem 3.17 we conclude without proof that VSP(F,10) should be the 4-fold of lines on another cubic 4-fold. We correct this in the e-print "Addendum to K3 surfaces of genus 8 and varieties of sums of powers of cubic fourfolds" (math.AG/0611533), where we establish that the general VSP(F,10) is in fact a new symplectic 4-fold different from the family of lines on a cubic 4-fold.