Seminar on Arithmetic Geometry

Speaker: Junliang Shen (ETH)

Date, time & place: January 18, 2016, 10:15 am, WSC-N-U-3.05

Title:Enumerative geometry of 3-folds and algebraic cobordism.

Abstract:  The enumerative geometry of a compact Calabi-Yau 3-fold plays a crucial role in mathematics and physics. Recently important progress has been made by Bridgeland, who proved that partition functions of Pandharipande-Thomas invariants for CY 3-folds are rational and satisfy a q~1/q symmetry. We generalize this property to all projective nonsingular 3-folds using ideas from algebraic cobordism. We consider cobordism invariants obtained by pushing forward the virtual cobordism class of the moduli space to a point. The partition function of cobordism invariants are conjectured to be rational and satisfy a functional equation. Finally I will explain the proof of the rationality for toric 3-folds.