Description
Mathematics Colloquium Talk II.
Speaker: Amalendu Krishna.
Affiliation: TIFR, Mumbai.
Date and Time: Wednesday 25 September, 2:45 pm - 3:45 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Revisiting Bertini theorems.
Abstract: The classical Bertini theorem in algebraic geometry says that a
general hyperplane section of a smooth quasi-projective subvariety of a
projective space over an algebraically closed field is also smooth. It was
already known long time ago that such a result holds over any infinite
field. However, this turned out to be false over finite field, as Katz
showed. Poonen then showed that Bertini theorem can be salvaged over
finite fields by allowing hypersurfaces of large degree rather than just
hyperplanes. In this talk, we shall revisit these Bertini theorems. In
particular, we shall prove new Bertini theorems for normal and integral
schemes over finite fields. This is based on a joint work with Mainak
Ghosh.