-
1
Calabi-Yau Manifolds Over Finite Fields, I
Published 2000“…We study Calabi-Yau manifolds defined over finite fields. These manifolds have parameters, which now also take values in the field and we compute the number of rational points of the manifold as a function of the parameters. …”
Book section -
2
Max Kreuzer's Contributions to the Study of Calabi-Yau Manifolds
Published 2012“…This is a somewhat personal account of the contributions of Max Kreuzer to the study of Calabi-Yau manifolds and has been prepared as a contribution to the Memorial Volume: Strings, Gauge Fields, and the Geometry Behind - The Legacy of Maximilian Kreuzer, to be published by World Scientific.…”
Book section -
3
Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry
Published 2001“…Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror X. …”
Book section -
4
The moduli space of complex Lagrangian submanifolds
Published 1999“…Following an earlier paper on the differential-geometric structure of the moduli space of special Lagrangian submanifolds in a Calabi-Yau manifold, we follow an analogous approach for compact complex Lagrangian submanifolds of a (K\"ahlerian) complex symplectic manifold. …”
Book section -
5
Singularities of special Lagrangian submanifolds
Published 2003“…We survey what is known about singularities of special Lagrangian submanifolds (SL $m$-folds) in (almost) Calabi-Yau manifolds. The bulk of the paper summarizes the author's work [18-22] on SL $m$-folds $X$ with isolated conical singularities. …”
Book section -
6
Singularities of special Lagrangian submanifolds
Published 2003“…We survey what is known about singularities of special Lagrangian submanifolds (SL m-folds) in (almost) Calabi-Yau manifolds. The bulk of the paper summarizes the author's five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0302356, math.DG/0303272 on SL m-folds X with isolated conical singularities. …”
Book section