Collapsing D-branes in Calabi-Yau moduli space I

We study the quantum volume of D-branes wrapped around various cycles in Ca labi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phase transitions between dis tinct low energy physical descriptions of the resulting string theory. Wher eas previous studies have solely considered quantum volumes in the context of two-cycles in perturbative string theory or D-branes in the specific exa mple of the quintic hypersurface, we work more generally and find qualitati vely new features. On the mathematical side, as we briefly note, our work h as some interesting implications for certain issues in arithmetic. (C) 2001 Published by Elsevier Science B.V.