Tadpole cancellation in Sen limits in F-theory was recently studied by Aluffi and Esole. We extend their results, generalizing the elliptic fibrations they used and obtaining a new case of universal tadpole cancellation, at least numerically. We coul
d not find an actual Sen limit having the correct brane content, and we argue that such a limit may not exist. We also give a uniform description of the fibration used by Aluffi and Esole as well as a new, simple, fibration which has non-Kodaira type fibers.
A main issue in superstring theory are the superstring measures. DHoker and Phong showed that for genus two these reduce to measures on the moduli space of curves which are determined by modular forms of weight eight and the bosonic measure. They als
o suggested a generalisation to higher genus. We showed that their approach works, with a minor modification, in genus three and we announced a positive result also in genus four. Here we give the modular form in genus four explicitly. Recently S. Grushevsky published this result as part of a more general approach.
