|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
How to determine the sign of a valuation on C[x,y]? | | Pinaki Mondal
; | | Date: |
14 Jan 2013 | | Abstract: | Given a divisorial discrete valuation ’centered at infinity’ on C[x,y], we
show that its sign on C[x,y] (i.e. whether it is negative or non-positive on
non-constant polynomials) is completely determined by the sign of its value on
the ’last key form’ (key forms being the avatar of ’key polynomials’ of
valuations (introduced by [Maclane, 1936]) in ’global coordinates’). The proof
involves computations related to the cone of curves on certain
compactifications of C^2 and gives a characterization of the divisorial
valuations centered at infinity whose ’skewness’ can be interpreted in terms of
the ’slope’ of an extremal ray of these cones, yielding a generalization of a
result of [Favre-Jonsson, 2007]. A by-product of these arguments is a
characterization of valuations which ’determine’ normal compactifications of
C^2 with one irreducible curve at infinity in terms of an associated ’semigroup
of values’. | | Source: | arXiv, 1301.3172 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER