Séminaire de géométrie algébrique

Virt: Zhixin Xie (Nice): Rationally connected threefolds with nef anticanonical divisor

001 (batiment I)


batiment I

Département de mathématiques Bâtiment I Faculté des Sciences 2 Boulevard Lavoisier F-49045 Angers cedex 01 France

Complex projective varieties with nef anticanonical divisor appear as natural generalisations of Fano varieties. Fano manifolds are classified up to dimension three and many of their properties are well studied. However, the classification of manifolds with nef anticanonical divisor is more complicated as new phenomena arise and many results for Fano manifolds no longer hold for this class of varieties. In this talk, we will first look at some examples in dimension two case. Then we will discuss some properties of rationally connected threefolds with nef anticanonical divisor. We will consider the case where the anticanonical divisor is not semi-ample, and by investigating the base locus of the anticanonical system, we will give a classification result in this case.