Bundles over the Fano Threefold V₅

ABSTRACT

Using an explicit resolution of the diagonal for the variety V ₅, we provide cohomological characterizations of the universal and quotient bundles. A splitting criterion for bundles over V ₅ is also proved.

The presentation of semistable aCM bundles is shown, together with a resolution–theoretic classification of low rank aCM bundles.

Key Words:

• aCM sheaves
• Cohomological characterization of bundles
• Fano threefold V ₅
• Quasi-homogeneous varieties
• Resolution of the diagonal
• Splitting criteria
• Vanishing intermediate cohomology

2000 Mathematics Subject Classification:

• 14F05
• 14J30
• 14J45
• 14J60
• 14D20

ACKNOWLEDGMENTS

The author would like to express his gratitude to Enrique Arrondo, Laura Costa, and Beatriz Graña for many useful suggestions, and Giorgio Ottaviani for his constant support. Also he would like to thank the Departments of Universitat de Barcelona and Universidad Complutense de Madrid for the friendly hospitality.

The author was partially supported by Italian Ministry funds and the EAGER contract HPRN-CT-2000-00099.

Notes

^# Communicated by R. Piene.