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