Addendum to "K3-surfaces of genus 8 and varieties of sums of powers of cubic fourfolds"

Details Addendum to "K3-surfaces of genus 8 and varieties of sums of powers of cubic fourfolds" Addendum to "K3-surfaces of genus 8 and varieties of sums of powers of cubic fourfolds"

2006-11-17

arxiv.org/abs/math/0611533v1

Mathematics

Algebraic Geometry

4 pages

Scientific paper

In this note, which is an addendum to the e-print math.AG/9810121, we prove 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, which is deformation equivalent to the Hilbert square of a K3 surface of genus 8 but different from the family of lines on a cubic 4-fold. This provides a new geometric construction of a compact complex symplectic fourfold, different from a Hilbert square of a K3 surface, a generalized Kummer 4-fold, the variety of lines on a cubic 4-fold and the recent examples of O'Grady (see Duke Math. J. 134, no. 1 (2006), 99-137).

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