Abstract
We clarify the undecided case c2 = 3 of a result of Ein, Hartshorne and Vogelaar [8] 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).
Reference18 articles.
1. [1] C. Anghel, I. Coand˘a, and N. Manolache, Globally generated vector bundles with small c1 on projective spaces. Mem. Amer. Math. Soc. 253 (2018), 1209, Providence, American Mathematical Society (AMS).
2. [2] C. Anghel, I. Coand˘a, and N. Manolache, Globally generated vector bundles with c1 = 5 on P3. Preprint arXiv:1805.11336 [math.AG].
3. [3] W. Barth, Some properties of stable rank-2 vector bundles on Pn. Math. Ann. 226 (1977), 125-150.
4. [4] W. Barth and K. Hulek, Monads and moduli of vector bundles. Manuscripta Math. 25 (1978), 323-347.
5. [5] A.A. Beilinson, Coherent sheaves on Pn and problems of linear algebra (Russian). Funktsional. Anal. i Prilozhen. 12 (1978), 3, 68-69. English translation in: Funct. Anal. Appl. 12 (1978), 214-216.