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Jeong-Seop Kim, Stability of Symmetric Powers of Vector Bundles on a Curve
May 13 @ 11:00 am - 12:00 pm KST
B266, IBS Korea, Republic of
For a stable vector bundle E on a smooth projective curve, it is known that the symmetric powers Sk E are semi-stable and are stable for all k > 0 in sufficiently general. Moreover, if E has rank 2, then Sk E is destabilized by a line subbundle if and only if the ruled surface PC(E) admits a k-section of zero self-intersection. In this talk, concentrating on the case of rank 2, we will find answers to the questions of which E has strictly semi-stable Sk E, and how many such E there are. Also, we will introduce relations between such E and the orthogonal bundles when k = 2, and Nori’s finite bundles when k ≥ 3.