Zero-Separating Invariants for Linear Algebraic Groups. Issue 4 (22nd December 2015)
- Record Type:
- Journal Article
- Title:
- Zero-Separating Invariants for Linear Algebraic Groups. Issue 4 (22nd December 2015)
- Main Title:
- Zero-Separating Invariants for Linear Algebraic Groups
- Authors:
- Elmer, Jonathan
Kohls, Martin - Abstract:
- Abstract: Abstract Let G be a linear algebraic group over an algebraically closed field 𝕜 acting rationally on a G -module V with its null-cone. Let δ( G, V ) and σ( G, V ) denote the minimal number d such that for every and, respectively, there exists a homogeneous invariant f of positive degree at most d such that f ( v ) ≠ 0. Then δ( G ) and σ( G ) denote the supremum of these numbers taken over all G -modules V . For positive characteristics, we show that δ( G ) = ∞ for any subgroup G of GL2 (𝕜) that contains an infinite unipotent group, and σ( G ) is finite if and only if G is finite. In characteristic zero, δ( G ) = 1 for any group G, and we show that if σ( G ) is finite, then G 0 is unipotent. Our results also lead to a more elementary proof that β sep ( G ) is finite if and only if G is finite.
- Is Part Of:
- Proceedings of the Edinburgh Mathematical Society. Volume 59:Issue 4(2016)
- Journal:
- Proceedings of the Edinburgh Mathematical Society
- Issue:
- Volume 59:Issue 4(2016)
- Issue Display:
- Volume 59, Issue 4 (2016)
- Year:
- 2016
- Volume:
- 59
- Issue:
- 4
- Issue Sort Value:
- 2016-0059-0004-0000
- Page Start:
- 911
- Page End:
- 924
- Publication Date:
- 2015-12-22
- Subjects:
- invariant theory, -- linear algebraic groups, -- geometrically reductive, -- prime characteristic, -- global degree bounds
Primary 13A50
Mathematics -- Periodicals
510 - Journal URLs:
- http://journals.cambridge.org/action/displayJournal?jid=PEM ↗
- DOI:
- 10.1017/S0013091515000322 ↗
- Languages:
- English
- ISSNs:
- 0013-0915
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library STI - ELD Digital store
- Ingest File:
- 1942.xml