Date: Tuesday, November 29, 2016
Location: 1096 East Hall (3:10 PM to 4:00 PM)
Title: Rational curves on hypersurfaces
Abstract: It is a well known fact that a general hypersurface of degree d in projective nspace is rationally connected if d is at most n, but contains very few curves if d is larger than n. More generally let X be a smooth projective variety and H a hypersurface of X such that K_X+H is antiample, then by the adjunction formula and a classical result of KollarMiyaokaMori we know that H is rationally connected. In a recent project we use the minimal model program as well as other techniques in birational geometry to study further how the behavior of rational curves on X as well as the positivity of (K_X + H) and H influence the behavior of rational curves in H. In this talk I will present several results and examples of this kind. In particular we will see criteria for uniruledness and rational connectedness of H.
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Speaker: Yuan Wang
Institution: University of Utah
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