Stable rank 3 vector bundles on ℙ³ with c₁ = 0, c₂ = 3

2021/03/22 by Coanda, Iustin
#14F06 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 14J60 #Secondary: 14D20

paper · doi:10.48550/arxiv.2103.11723

Abstract

We clarify the undecided case c₂ = 3 of a theorem of Ein, Hartshorne and Vogelaar [Math. Ann. 259 (1982), 541--569] about the restriction of a stable rank 3 vector bundle with c₁ = 0 on the projective 3-space to a general plane. It turns out that there are more exceptions to the stable restriction property than those conjectured by the three authors. One of them is a Schwarzenberger bundle (twisted by -1); it has c₃ = 6. There are also some exceptions with c₃ = 2 (plus, of course, their duals). We also prove, for completeness, the basic properties of the corresponding moduli spaces; they are all nonsingular and connected, of dimension 28.

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