Understand
In this paper, we study boundedness questions for (simply-connected) smooth Calabi-Yau threefolds.
- The diffeomorphism class of such a threefold is known to be determined up to finitely many possibilities by the integral middle cohomology and two integral forms on the integral second cohomology, namely the cubic cup-product form and the linear form given by cup-product with the second Chern class.
- The motivating question for this paper is whether knowledge of these cubic and linear forms determines the threefold up to finitely many families, that is the moduli of such threefolds is bounded.
- If this is true, then in particular the middle integral cohomology would be bounded by knowledge of these two forms on the second cohomology.