Eleonora Romano

Title: The "Positivity Problem": an introduction and recent developments

Abstract: Given a morphism with connected fibers between normal  
projective varieties, it is a natural problem to try to relate  
positivity properties between the anticanonical divisors of the  
varieties. In this talk, we first recall some known results on this  
subject. Then we focus on the case in which the morphism is a Fano  
conic bundle, i.e. a fiber type contraction of a Fano manifold, where  
every fiber is one-dimensional. We discuss some recent results about  
Fano conic bundles, and we give new examples of such contractions  
which allow us to deduce something more about the “Positivity Problem”.