Abstract
Tadpole cancellation in F-theory on an elliptic Calabi-Yau fourfold X→B3 demands some spacetime-filling three-branes (points in B3). If moved to the discriminant surface, which supports the gauge group, and dissolved into a finite size instanton, the second Chern class of the corresponding bundle E is expected to give a compensating contribution. However the dependence of D-brane charge on the geometry of W and on the embedding i:W→B3 gives a correction to c2(E). We show how this is reconciled by considering the torsion sheaf i*E and discuss some integrality issues related to global properties of X as well as the moduli space of this object.