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arXiv · 1207.1159

Linear subspaces, symbolic powers and Nagata type conjectures

Marcin Dumnicki·Brian Harbourne·Tomasz Szemberg·Halszka Tutaj-Gasińska
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Abstract

Prompted by results of Guardo, Van Tuyl and the second author for lines in projective 3 space, we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r dimensional planes in projective n space for n at least 2r+1. These considerations lead to new conjectures that suggest that the well known conjecture of Nagata for points in the projective plane is not sporadic, but rather a special case of a more general phenomenon.

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Marcin Dumnicki, Brian Harbourne, Tomasz Szemberg, Halszka Tutaj-Gasińska. 2012-09-30. Linear subspaces, symbolic powers and Nagata type conjectures. https://doi.org/10.1016/j.aim.2013.10.029

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