Speaker: Ananyo Dan
Date: January 28, 2016
Affiliation: TIFR

Abstract: For an integer $d \ge 4$, the Noether-Lefschetz theorem tells us that a very general smooth degree d surface in $\mathbb{P}^3$ has Picard number equal to one. We define Noether-Lefschetz locus to be the space parametrizes smooth degree $d$ hypersurfaces in $\mathbb{P}^3$ with Picard number at least 2 i.e., violating the Noether-Lefschetz theorem. As part of my Ph.D., I studied various relations between the geometry of the Noether-Lefschetz locus and that of the Hilbert schemes of curves. I try to review existing and new results in this direction.