Spectrum bounds in geometry

TL;DR

This paper investigates the bounds on geometric quantities in F-theory Calabi-Yau compactifications, building on prior results about elliptically fibered Calabi-Yau threefolds, and provides explicit bounds.

Contribution

It extends the work on topological finiteness to explicit bounds on geometric quantities in F-theory compactifications.

Findings

Established explicit bounds on geometric quantities

Connected topological finiteness to physical spectrum constraints

Provided a framework for analyzing F-theory compactifications

Abstract

Filipazzi, Hacon and Svaldi proved that there are only finitely many topological types of elliptically fibered Calabi-Yau threefolds. We explore the implications of their results on the boundedness of the geometric quantities in the massless spectrum of the F-theory Calabi-Yau compactifications. We conclude with explicit bounds.