Stable rank 2 reflexive sheaves on P^3 with large c_3

Abstract

The subject of reflective sheaves, in particular, rank 2 reflective sheaves on P^3, has recently received some attention, both in its own right and as a tool in the study of vector bundles and curves [1], [2], [3], [6]. The existence of moduli spaces for stable sheaves has been established by Maruyama [5]. A stable rank 2 reflective sheaf on P^3 has Chern classes c_1, c_2, c_3 ϵ Z. It is known that c_3 is essentially the number of non-locally-free points E and that if E is normalized, i.e., if c_1 = 0 (respective, c_1 = -1), we have c_2 > 0, 0 ≤ c_3 ≤ c2/2 – c_2 + 2, (resp. 0 ≤ c_3 ≤ c2/2), and c_3 is even (resp. c_3 = c_2 mod 2) [3] 3.3, 8.2, 2.4. In [3], Hartshorne studies the moduli spaces of stable rank 2 reflective sheaves with c_1 = -1, and the maximal c_3, i.e., c_3 = c2/2.

Additional details