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Aug 9, 2014 at 10:49 comment added user27920 @NadimRustom: see section B.2.2 of the preprint uni-due.de/~ade847f/bdp5
Dec 9, 2013 at 23:04 comment added David Zureick-Brown @NadimRustom: You can also have D1-D2 on a usual curve with degree 1 but no sections (i.e., not equivalent to an effective divisor).
Oct 8, 2013 at 11:21 comment added Nadim Rustom @DavidLoeffler: Thanks, yes that sounds quite reasonable. I just found it surprising that on stacks, an invertible sheaf can have positive degree without having global sections.
Oct 8, 2013 at 11:02 history edited Olivier CC BY-SA 3.0
Corrected grammar
Oct 8, 2013 at 10:05 comment added David Loeffler If the degree of $\omega$ weren't strictly positive, then not only would there be no weight 1 cusp forms for $\Gamma_0(1)$, but there would be no weight 1 cusp forms for any level whatsoever, because pullback via a finite flat morphism will just multiply the degree of $\omega$ by a positive constant. Does that answer your (1)?
Oct 8, 2013 at 8:25 history asked Nadim Rustom CC BY-SA 3.0