Cocharacter-closure and the rational Hilbert-Mumford Theorem

TY - JOUR

T1 - Cocharacter-closure and the rational Hilbert-Mumford Theorem

AU - Bate, Michael Edward

AU - Herpel, Sebastian

AU - Martin, Benjamin

AU - Roehrle, Gerhard

N1 - © Authors, 2016

PY - 2017/11/10

Y1 - 2017/11/10

N2 - For a field k, let G be a reductive k-group and V an affine k-variety on which Gacts. Using the notion of cocharacter-closed G(k)-orbits in V, we prove a rational versionof the celebrated Hilbert–Mumford Theorem from geometric invariant theory. We initiate astudy of applications stemming from this rationality tool. A number of examples are discussedto illustrate the concept of cocharacter-closure and to highlight how it differs from the usualZariski-closure.

AB - For a field k, let G be a reductive k-group and V an affine k-variety on which Gacts. Using the notion of cocharacter-closed G(k)-orbits in V, we prove a rational versionof the celebrated Hilbert–Mumford Theorem from geometric invariant theory. We initiate astudy of applications stemming from this rationality tool. A number of examples are discussedto illustrate the concept of cocharacter-closure and to highlight how it differs from the usualZariski-closure.

KW - Affine G-variety

KW - Cocharacter-closed orbit

KW - Rationality

UR - http://www.scopus.com/inward/record.url?scp=84994766905&partnerID=8YFLogxK

U2 - 10.1007/s00209-016-1816-5

DO - 10.1007/s00209-016-1816-5

M3 - Article

SN - 0025-5874

VL - 287

SP - 39

EP - 72

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 1-2

ER -