MATH Seminar
| Title: Splitting projective modules using Chern classes |
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| Seminar: Algebra and Number Theory |
| Speaker: Jean Fasel of LMU Munich |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-11-15 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: Let $X$ be a smooth affine variety of dimension $d$ over a field $k$ and let $E$ be a vector bundle of rank $r$. If $E$ splits off a free bundle of rank 1, then the Chern class $c_r(E)$ is trivial. If the base field $k$ is algebraically closed and $r=d$ then M.P.~Murthy (with N.~Mohan Kumar when $d=3$) proved that the converse statement holds. In this talk, we will discuss more general situations, namely $r=d$ over arbitrary fields and $r=d-1$ over algebraically closed fields. |
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