On moduli spaces of semistable sheaves on Enriques surfaces

Volume 99 / 2010

Marcin Hauzer Annales Polonici Mathematici 99 (2010), 305-321 MSC: Primary 14D20; Secondary 14J28. DOI: 10.4064/ap99-3-7


We describe some one-dimensional moduli spaces of rank $2$ Gieseker semistable sheaves on an Enriques surface improving earlier results of H. Kim. In the case of a nodal Enriques surface the moduli spaces obtained are reducible for general polarizations. For unnodal Enriques surfaces we show how to reduce the study of moduli spaces of high even rank Gieseker semistable sheaves to low ranks. To prove this we use the method of K. Yoshioka who showed that in the odd rank case, one can reduce to rank $1$.


  • Marcin HauzerInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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