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I am sorry to make this a new question. I would have liked to leave a comment, but I suppose I don't have enough rep for that....

So, in the accepted answer to this question I don't understand why in the second term it is $\dim H^0(X,L\otimes \Lambda^{0,1})$ and not $L^{-1}$ with the same.thing. I suspect this is some Hodge theory thing that I am not recognizing, and it is probably completely trivial, but I would appreciate if someone could enlighten me.

Thank you.

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closed as too localized by Cam McLeman, Daniel Moskovich, Loop Space, Tim Perutz, Pete L. Clark Nov 3 '10 at 15:17

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

I think you are right. It should be $ind (\partial_L)=dim H^0 (X;L) - dim H^0 (X;L^{-1} \otimes \Lambda^{0,1})$, the second summand is dual to the cokernel of $\partial_L$ by Serre duality. – Johannes Ebert Nov 2 '10 at 8:16
I both upvoted, and voted to close. So you would have enough rep to repost this good question as a comment. – Daniel Moskovich Nov 2 '10 at 11:30
Thank you for that. I made the comment where it belonged. Since I am new to MO, I am not sure what I should do now. Should I delete this, or "vote to close"? Or just wait for the moderators to take action? Thanks. – Alfonz Nov 3 '10 at 0:08
I made a comment on the accepted answer to the other question (I also agree with you). I want to give people (especially the answerer) a little time to respond, and then I or someone else can simply edit the answer. @Alfonz: perhaps it is best for you to wait until the answer is corrected (or the situation is otherwise resolved) and then delete this question. – Pete L. Clark Nov 3 '10 at 15:24
@Pete: OK, thanks. – Alfonz Nov 3 '10 at 15:57