Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $X$ a smooth projective curve over $\mathbb{C}$, $S$ a finite subscheme of $X$.

$E$ a vector bundle over $X$ with a divisor $D$. We look at the sections $A:=H^{0}(X,E)$ with $\deg E$ big enough.

Is it true, that the set $A^{0}_{S}$ consisting of sections that meet transversally $D$ and avoid $D$ at the points of $S$ is an open subset? And what should be the bound for $\deg E$ so that it holds?

share|improve this question
A section of $E$ cannot meet a point in $D$ transversally unless it avoids it. Is this what you have in mind ? –  Damian Rössler Apr 5 '13 at 7:52
I mean that for a point $x\in X$ and $s$ a section of $E$, either $x\in S$ and the $s(x)\notin D$, either $x\in X-S$ and then s(x) needs to meet transversally $D$. –  prochet Apr 6 '13 at 16:20

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.