On the Tropicalization of the Hilbert Scheme

Rapport Preprint On the Tropicalization of the Hilbert Scheme eng 2009 author Alessandrini Daniele author Nesci Michèle 706824 19 0912.0082v1 In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on the degree of the elements of a tropical basis of an ideal in terms of its Hilbert polynomial. As corollary, we prove that the set of tropical varieties defined over an algebraically closed valued field only depends on the characteristic pair of the field and the image group of the valuation. In conclusion, we examine some simple examples that suggest that the definition of tropical variety should include more structure than what is currently considered. Dewey 510 arxiv math.AG 25 Section de mathématiques 11 false ce837937-bcbc-4f2e-945e-3d96026f4eee Preprint Public 0912.0082v1.pdf 264592 application/pdf openAccess Faculté des sciences / Section de mathématiques

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On the Tropicalization of the Hilbert Scheme				2009	557	229

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Nesci, Michèle