Liana Heuberger (Nice)
Fano varieties, general elephants and classification
We give an overview on how and why we classify Fano varieties. The smooth case is known up to dimension three, and we discuss the role that the general elephant, i.e. a general divisor D in | -K_X |, plays in this classification. We state the problem and current advances in dimension four. We then investigate what happens if we allow the Fano variety to have mild singularities and why this makes sense in the bigger picture of classification of algebraic varieties.