# Coniveau Seminar

This is a seminar on the coniveau filtration in various context. We will attempt to understand two major advances in this subject

1. Two coniveau filtrations (Benoist-Ottem)
2. On the coniveau of rationally connected threefolds (Voisin)

Schedule

We meet at 11am Eastern at https://harvard.zoom.us/j/96701460837?pwd=SDQ2dWlmVnpxTzFYN3VaY05nYTdLdz09

• (Feb 12) Two Coniveau filtrations (JCO) Abstract: A cohomology class of a smooth complex variety of dimension n has coniveau $\geq c$ if it vanishes in the complement of a closed subvariety of codimension $\geq c$, and has strong coniveau $\geq c$ if it comes by proper pushforward from the cohomology of a smooth variety of dimension $\leq n-c$. In a paper with Olivier Benoist, we show that these two notions differ in general, both for integral classes on smooth projective varieties and for rational classes on smooth open varieties. This talk will give a gentle introduction to the subject, with lots of examples. (Notes from JCO)
• (Feb 26) Section 2 of Benoist-Ottem (Elden)
• (March 5) Section 3 of Benoist-Ottem (Mura)
• (March 19) Sections 4 of Benoist-Ottem
• (April 2) Section 5 of Benoist-Ottem (Dori)
• (April 16) Section 6 of Benoist-Ottem (Dori)
• (April 30) Section 1 of Voisin