On the Semistability of Instanton Sheaves Over Certain Projective Varieties

Abstract

We show that instanton bundles of rank r ≤ 2n − 1, defined as the cohomology of certain linear monads, on an n-dimensional projective variety with cyclic Picard group are semistable in the sense of Mumford–Takemoto. Furthermore, we show that rank r ≤ n linear bundles with nonzero first Chern class over such varieties are stable. We also show that these bounds are sharp.

Key Words:

• Monads
• Semistable sheaves

2000 Mathematics Subject Classification:

• 14J60
• 14F05

ACKNOWLEDGMENTS

The first author is partially supported by the FAEPEX grants number 1433/04 and 1652/04 and the CNPq grant number 300991/2004-5. The second author is partially supported by the grant MTM2004-00666.

Notes

Communicated by R. Piene.