On the Stability of the Restricted Bundle of Space Curves Contained in a Quartic Surface
نویسنده
چکیده
Here we show the existence of a smooth complex projective curve Z P 3 of degree d and genus g such that TP 3 jZ is stable for all integers d; g such that (roughly) d 2 =9 < g < (d?1) 2 =8. Following a construction of Gruson and Peskine we will nd such a curve Z on an integral rational quartic surface with a double line. We will use in an essential way also the main properties of stable vector bundles on reduced (but reducible) curves. In this way we will obtain examples of space curves with restricted tangent bundle with high degree of stability. Then for n = 3; 4 and 5 we will construct curves in P n with simple restricted tangent bundle for all invariants (d; g) with (roughly) 2d g d 2 =(4n?4) and contained in a surface of degree 2n ? 2.
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