Title: "Blow-ups of a quadric in P^4 along a curve yielding weak Fano threefolds".

 Abstract: 

In this talk, we will examine the question of when the blow-up of a smooth quadric hypersurface in P^4 along a smooth, irreducible curve is weak Fano. We are able to give a complete answer depending only on some conditions on the geometry of the curve, particularly its degree and genus. We will introduce the notions, most importantly those of (weak) Fano threefolds, that are necessary in order to formulate the corresponding result and give the main ideas of its proof.

https://www.unine.ch/math/seminaire-algebre-et-geometrie-de-neuchatel/