Varieties of sums of powers

Details Varieties of sums of powers Varieties of sums of powers

1998-01-23

arxiv.org/abs/math/9801110v2

J. Reine Angew. Math. 525 (2000) 147--181

Mathematics

Algebraic Geometry

Final published version (Crelle)

Scientific paper

The variety of sums of powers of a homogeneous polynomial of degree d in n variables is defined and investigated in some examples, old and new. These varieties are studied via apolarity and syzygies. Classical results of Sylvester (1851), Hilbert (1888), Dixon and Stuart (1906) and some more recent results of Mukai (1992) are presented together with new results for the cases (n,d)=(3,8), (4,2), (5,3). In the last case the variety of sums of 8 powers of a general cubic form is a Fano 5-fold of index 1 and degree 660.

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