A presentation of a degree d form in n+1 variables as the sum of homogenous elements "essentially" involving n variables is called a codimen- sion one decomposition. Codimension one decompositions are introduced and the related Waring Problem is stated and solved. Natural schemes describing the codimension one decompositions of a generic form are dened. Dimension and degree formulae for these schemes are derived when the number of summands is the minimal one; in the zero dimensional case the scheme is showed to be reduced. These results are obtained by studying the Chow variety Dn;s of zero dimensional degree s cycles in Pn. In particular, an explicit formula for degDn;s is determined.

Codimension one decompositions and Chow varieties / Carlini, Enrico. - (2005), pp. 67-79. (Intervento presentato al convegno Projective varieties with unexpected properties).

Codimension one decompositions and Chow varieties.

CARLINI, ENRICO
2005

Abstract

A presentation of a degree d form in n+1 variables as the sum of homogenous elements "essentially" involving n variables is called a codimen- sion one decomposition. Codimension one decompositions are introduced and the related Waring Problem is stated and solved. Natural schemes describing the codimension one decompositions of a generic form are dened. Dimension and degree formulae for these schemes are derived when the number of summands is the minimal one; in the zero dimensional case the scheme is showed to be reduced. These results are obtained by studying the Chow variety Dn;s of zero dimensional degree s cycles in Pn. In particular, an explicit formula for degDn;s is determined.
2005
9783110181609
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1724868
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