The Fu-Yau equation with negative slope parameter

Abstract

The Fu-Yau equation is an equation introduced by J. Fu and S.T. Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter ${\alpha }^{\prime }$. The equation was solved in dimension $2$ by Fu and Yau in two successive papers for ${\alpha }^{\prime }>0$, and for ${\alpha }^{\prime }<0$. In the present paper, we solve the Fu-Yau equation in arbitrary dimension for ${\alpha }^{\prime }<0$. To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater than $2$.

30 pages, final version, to appear in Invent. Math

References in corpus (3)

• Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton
• A Construction of Non-Kähler Calabi-Yau Manifolds and New Solutions to the Strominger System
• Weak solutions of complex Hessian equations on compact Hermitian manifolds

Cited by in corpus (2)

• Hessian equations on closed Hermitian manifolds
• The Anomaly flow over Riemann surfaces