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We study Le Potier's strange duality on del Pezzo surfaces using quot schemesto construct independent sections of theta line bundles on moduli spaces ofsheaves, one of which is the Hilbert scheme of n points. For n at most 7, weuse multiple point formulas to count the length of the quot scheme, whichagrees with the dimension of the space of sections on the Hilbert scheme. Whenthe surface is the projective plane and n is arbitrary, we use nice resolutionsof general stable sheaves to show that the quot schemes that arise are finiteand reduced. Combining our results, we obtain a lower bound on the rank of thestrange duality map, as well as evidence that the map is injective when n is atmost 7.

Le Potier's strange duality, quot schemes, and multiple point formulas for del Pezzo surfaces