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Acta Mathematica Vietnamica

DEFORMATIONS OF THE TANGENT BUNDLE AND THEIR RESTRICTION TO STANDARD RATIONAL CURVES

icon-email JUN-MUK HWANG

Abstract

We study the deformations of the tangent bundle of a uniruled manifold $X$ by restricting them to standard rational curves on $X$. By employing an idea from holomorphic symplectic geometry, we prove that, if $H^{2i}(X, \Omega^1_X) = 0$ for all $i \geqslant 0$, the splitting type on a standard rational curve remains unchanged under small deformations of the tangent bundle.