A mathematical instanton bundle on P (over an algebraically closed field) is a rank two vector bundle ε on P with c = 0 and with H (ε) = H (ε(-2)) = 0. Let c (ε) = n. Then n > 0. A jumping line of ε of order a, (a > 0), is a line ℓ in P on which ε splits as script O sign (-a)⊕script O sign (a). It is easy to see that the jumping lines of ε all have order ≤ n. We will say that ε has a maximal order jumping line if it has a jumping line of order n. Our goal is to show that such an ε is unobstructed in the moduli space of stable rank two bundles, i.e., H (ε ⊗ ε) = 0. The technique can be slightly extended. We show that when c = 5, any ε with a jumping line of order 4 is unobstructed. We describe at the end how mathematical instantons with maximal order jumping lines arise and estimate the dimension of this particular smooth locus of bundles. 3 3 0 1 3 2 1 2 ℓ ℓ 2
Pacific Journal of Mathematics
Rao, A. Prabhakar, "Mathematical instantons with maximal order jumping lines" (1997). Mathematics and Statistics Faculty Works. 8.
Available at: https://irl.umsl.edu/mathstats-faculty/8