Atiyah Classes and Closed Forms on Moduli Spaces of Sheaves

  • Francesco Bottacin

    Università di Padova, Italy


Let be a smooth -dimensional projective variety, and let be a moduli space of stable sheaves on . By using the local Atiyah class of a universal family of sheaves on , which is well defined even when such a universal family does not exist, we are able to construct natural maps

for any and any . In particular, for , the map associates a closed differential form of degree on the moduli space to any element of . This method provides a natural way to construct closed differential forms on moduli spaces of sheaves. We remark that no smoothness hypothesis is made on the moduli space . As an application, we describe the construction of closed differential forms on the Hilbert schemes of points of .

Cite this article

Francesco Bottacin, Atiyah Classes and Closed Forms on Moduli Spaces of Sheaves. Rend. Sem. Mat. Univ. Padova 121 (2009), pp. 165–177

DOI 10.4171/RSMUP/121-10