The geometry of degenerations of Hilbert schemes of points

Autor: Ziyu Zhang, Klaus Hulek, Martin G. Gulbrandsen, Lars Halvard Halle

Publikováno v: Journal of Algebraic Geometry
Gulbrandsen, M G, Halle, L H, Hulek, K & Zhang, Z 2021, ' The geometry of degenerations of Hilbert schemes of points ', Journal of Algebraic Geometry, vol. 30, no. 1, pp. 1-56 . https://doi.org/10.1090/jag/765

Given a strict simple degeneration $f \colon X\to C$ the first three authors previously constructed a degeneration $I^n_{X/C} \to C$ of the relative degree $n$ Hilbert scheme of $0$-dimensional subschemes. In this paper we investigate the geometry of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9366077c51e144d1725c9f2f5828e3ad
https://doi.org/10.1090/jag/765

A relative Hilbert–Mumford criterion

Autor: Klaus Hulek, Martin G. Gulbrandsen, Lars Halvard Halle

Publikováno v: Manuscripta Mathematica. 148:283-301

We generalize the classical Hilbert-Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X -> Spec A to a noethe

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5dff5c002a9818567588de72d85d3a79
https://doi.org/10.1007/s00229-015-0744-8

Néron Models and Base Change

Autor: Lars Halvard Halle, Johannes Nicaise

Presenting the first systematic treatment of the behavior of Néron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to Néron models of semi-abelian varieties, motivat

Content of This Book

Autor: Johannes Nicaise, Lars Halvard Halle

Publikováno v: Néron Models and Base Change ISBN: 9783319266374

The aim of this book is to make a detailed analysis of the behaviour of Neron models of semi-abelian varieties under ramified base change, and apply the results to the study of motivic zeta functions. The main invariants we are interested in are the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9bd548af174527a937e3e2900a9d7e55
https://doi.org/10.1007/978-3-319-26638-1_1

The Base Change Conductor and Edixhoven’s Filtration

Autor: Johannes Nicaise, Lars Halvard Halle

Publikováno v: Néron Models and Base Change ISBN: 9783319266374

In this chapter, we recall the definition of the base change conductor of a semi-abelian K-variety G and of Edixhoven’s filtration on the special fiber of the Neron model of G. We use Edixhoven’s construction to define a new invariant, the tame b

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::08b50b169fd756ecf40f319ee1ab77e4
https://doi.org/10.1007/978-3-319-26638-1_6