A GIT construction of degenerations of Hilbert schemes of points

Autor:	Gulbrandsen, Martin G., Halle, Lars H., Hulek, Klaus
Rok vydání:	2016
Předmět:	Mathematics - Algebraic Geometry 14D06 (Primary) 14C05 14L24 14D23 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A comparison with the construction of Li and Wu shows that our GIT stack and the stack they construct are isomorphic, as are the associated coarse moduli schemes. Our construction is sufficiently explicit to obtain good control over the geometry of the singular fibres. We illustrate this by giving a concrete description of degenerations of degree $n$ Hilbert schemes of a simple degeneration with two components. Comment: 50 pages; to appear in Documenta Mathematica
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1604.00215 Zobrazit plný text záznamu View this record from Arxiv