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Apr 25, 2019 at 13:26 comment added Daniele A Thank you for the suggestion. Unfortunately, I think that this does not help since the morphism is not general: is the one induced by the differential of $f$.
Apr 23, 2019 at 17:14 comment added Sasha If $\phi \colon E \to F$ is a general morphism of vector bundles (i.e., general element in the vector space $\Hom(E,F)$) and if the bundle $E^\vee \otimes F$ is globally generated, then the corank 2 locus has expected codimension. Does that help?
Apr 23, 2019 at 13:50 comment added Daniele A Thank you Sasha. Indeed, I was aware of this, and in my case, I get a nonzero cohomology class. However my problem is more that the locus could be too big, hence I am looking at a lower bound for the codimension. Is there any way to get one?
Apr 23, 2019 at 11:59 history answered Sasha CC BY-SA 4.0