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Jul 20, 2012 at 16:11 comment added o a @Mahdi: be aware that the paper gets updated from time to time so you need to check ihes.fr/~gromov/topics/recent.html to find the most recent version (10 july as of now)...also, at the very end itmentions a result of Esnault-Viehweg ("Such ”rank inequalities” are reminiscent of inequalities for spaces of sections and (cohomologies in general) of positive vector bundles such e.g. as in the Khovanski-Teissier theorem and in the Esnault-Viehweg proof of the sharpened Dyson-Roth lemma, but a direct link is yet to be found") which appears close to your interests.
Jul 19, 2012 at 16:52 comment added Mahdi Majidi-Zolbanin Dear o a: Thank you for sharing this paper. I had not seen this paper, I will look at it.
Jul 19, 2012 at 15:53 history answered o a CC BY-SA 3.0