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

Aaron Bertram ^[1] ; Thomas Goller ^[1] ; Drew Johnson ^[2]
1. [1] University of Utah
  
  University of Utah
  
  Estados Unidos
2. [2] University of Utah, USA; Brigham Young University, USA
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 5, 2023
Idioma: inglés
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Resumen
- 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 ≤ 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 P2 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 ≤ 7.