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We consider a class of tautological top intersection products on the moduli space of stable pairs consisting of vector bundles together with  N  sections on a smooth complex projective curve  C . We show that when  N  is large, these intersection numbers can equally be computed on the Grothendieck Quot scheme of coherent sheaf quotients of the rank  N  trivial sheaf on  C . The result has applications to the calculation of the intersection theory of the moduli space of semistable bundles on  C .

On the intersection theory of Quot schemes and moduli of bundles with sections