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 curve over $\mathbb{C}$, $D$ a divisor on $X$, $R$ a local artinian ring of residue field $\mathbb{C}$

Let $A=H^{0}(X_{R},\mathcal{O}(D_{R}))$ the scheme of sections over $Spec(R)$.

Let $H\subset X_{R}$ an effective divisor such that his reduction over $\mathbb{C}$, $\bar{H}=[x]$ for a point $x\in X$. Fix an integer $N\in \mathbb{N}$, If $\deg(D)$ is big enough, do we have a smooth surjective morphism

$A\rightarrow \mathcal{O}(D_{R})\otimes_{\mathcal{O}_{X_{R}}}\mathcal{O}_{X_{R}}/I_{H}^{n}$


share|improve this question

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.