Abstract
The tangent bundle ℐX of a Calabi-Yau threefoldX is the only known example of a stable bundle with non-trivial restriction to any rational curve onX. By deforming the direct sum of ℐX and the trivial line bundle one can try to obtain new examples. We use algebro-geometric techniques to derive results in this direction. The relation to the finiteness of rational curves on Calabi-Yau threefolds is discussed.
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