Virtual Fundamental Classes of Zero Loci
  Let V be a convex vector bundle over a smooth projective manifold X, and let Y be the subset of X which is the zero locus of a regular section of V. This mostly expository paper discusses a conjecture which relates the virtual fundamental classes of X and Y. Using an argument due to Gathmann, we prove a special case of the conjecture. The paper concludes with a discussion of how our conjecture relates to the mirror theorems in the literature. 
David A. Cox (Amhert College), Sheldon Katz (Oklahoma State) and   Yuan-Pin Lee (UCLA)