On real Calabi-Yau threefolds twisted by a section

Abstract

We study the mod $2$ cohomology of real Calabi-Yau threefolds given by real structures which preserve the torus fibrations constructed by Gross. We extend the results of Castaño-Bernard-Matessi and Arguz-Prince to the case of real structures twisted by a Lagrangian section. In particular we find exact sequences linking the cohomology of the real Calabi-Yau with the cohomology of the complex one. Applying SYZ mirror symmetry, we show that the connecting homomorphism is determined by a ``twisted squaring of divisors'' in the mirror Calabi-Yau, i.e. by $D\mapsto D^2+DL$ where $D$ is a divisor in the mirror and $L$ is the divisor mirror to the twisting section. We use this to find an example of a connected $(M-2)$-real quintic threefold.

36 pages, 10 figures. Comments wellcome!

References in corpus (2)

• Real Lagrangians in Calabi-Yau Threefolds
• A Note on Schoen's Calabi--Yau Threefolds

Cited by in corpus (1)

• Mirror symmetry for tropical hypersurfaces and patchworking