Seminar

After Shigefumi Mori showed in his landmark works that many interesting varieties contain rational curves, their systematic study became a standard tool in algebraic geometry. The spectrum of applications is diverse and covers long-standing problems concerning deformation rigidity, stability of the tangent bundle, and classification. In this talk, we give a few examples that show how rational curves can be used to answer such problems. We also discuss existence criteria for rational curves, and show how these can be useful even in the study of spaces that are known to not contain any rational curves.