MATHEMATICAL INSTANTONS WITH MAXIMAL ORDER JUMPING LINES

A mathematical instanton bundle on P-3 (over sn algebraically closed f ield) is a rank two vector bundle E on P-3 with c(1) = 0 and with H-0( E) = H-1(E(-2)) = 0. Let c(2)(E) = n. Then n > 0. A jumping line of E of order a, (a > 0), is a line l in P-3 on which E splits as O-l(-a) O-l(a). It is easy to see that the jumping lines of E all have order less than or equal to n. We will say that E has a maximal order jumpin g line if it has a jumping line of order n. Our goal is to show that s uch an E is unobstructed in the moduli space of stable rank two bundle s, i.e., H-2(E x E) = 0. The technique can be slightly extended, We sh ow that when c(2) = 5, any E with a jumping line of order 4 is unobstr ucted. We describe at the end how mathematical instantons with maximal order jumping lines arise and estimate the dimension of this particul ar smooth locus of bundles.