Talk:Brill–Noether theory

Expansion[edit]

We can definitely expand the section on Brill-Noether theory to include some concrete statements as well as adding some references (viz. ACGH).

unclear[edit]

are particular, in the sense of determining more compatible functions than would be predicted.

compatible in what sense? predicted by whom? Crasshopper (talk) 03:52, 10 January 2011 (UTC)[reply]

incorrect?[edit]

On the page it says:

     There is a lower bound ρ for the dimension dim(n, r, g) of this subscheme in Pic(C):
     dim(n, r, g) ≥ ρ = r(n − r + 1) − (r − 1)g

This cannot be right. Pic(C) has dimension g so defenitly the left hand side is smaller then g. However the right hand side can defenitly be largen then g by taking n large enough! I don't know bril noether theory so I don't know how to fix it but I suspect that "this subscheme in Pic(C)" should instead be a subscheme of C^n or maybe the nth symmetric power of C.

Math Mind (talk) 18:41, 29 June 2012 (UTC)[reply]