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. A key ingredient is what we call the geometric anomaly equation, and the extension of the gravitational anomaly cancellation in physics, also to singular spaces. We review and extend the dictionary between geometry and physics. We conclude with explicit bounds.
Grassi, A. (2025). Spectrum bounds in geometry. Cambridge : Cambridge University Press [10.1017/9781009396233].
Spectrum bounds in geometry
Grassi, Antonella
2025
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. A key ingredient is what we call the geometric anomaly equation, and the extension of the gravitational anomaly cancellation in physics, also to singular spaces. We review and extend the dictionary between geometry and physics. We conclude with explicit bounds.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
