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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.


May 13
11:00 am - 12:00 pm KST
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IBS Korea, Republic of


Jaehyun Hong
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 복소기하학연구단
대전 유성구 엑스포로 55 (우) 34126
IBS Center for Complex Geometry
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
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