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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*S*are semi-stable and are stable for all^{k}E*k*> 0 in sufficiently general. Moreover, if*E*has rank 2, then*S*is destabilized by a line subbundle if and only if the ruled surface^{k}E*admits a***P**_{C}(E)*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*S*, and how many such^{k}E*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.