Birational aspects of the Geometry of Varieties of Sum of Powers

Details Birational aspects of the Geometry of Varieties of Sum of Powers Birational aspects of the Geometry of Varieties of Sum of Powers

2010-10-08

arxiv.org/abs/1010.1707v2

Mathematics

Algebraic Geometry

16 pages, corrected wrong attribution

Scientific paper

Varieties of Sums of Powers describe the additive decompositions of an homogeneous polynomial into powers of linear forms. Despite their long history, going back to Sylvester and Hilbert, few of them are known for special degrees and number of variables. In this paper we aim to understand a general birational behaviour of VSP, if any. To do this we birationally embed these varieties into Grassmannians and prove the rationality, unirationality or rational connectedness of many of those in arbitrary degrees and number of variables.

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