30 citations · 30 across the 2 of their papers we have counts for
7 papers · 1 filter
Toric Degenerations and Batyrev-Borisov Duality
Mark Gross
This is an extended example of the study of mirror symmetry via log schemes and the discrete Legendre transform on affine manifolds, introduced by myself and Bernd Siebert in "Mirr…
Mirror Symmetry via Logarithmic Degeneration Data I
Mark Gross, Bernd Siebert
This paper is the first arising from our project announced in math.AG/0211094, "Affine manifolds, log structures, and mirror symmetry." We aim to study mirror symmetry by studying…
Examples of Special Lagrangian Fibrations
Mark Gross
We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions…
Calabi-Yau Threefolds and Moduli of Abelian Surfaces I
Mark Gross, Sorin Popescu
We describe birational models and decide the rationality/unirationality of moduli spaces AA_{d} (and AA^{lev}_{d}) of (1,d)-polarized abelian surfaces (with canonical level structu…
Topological Mirror Symmetry
Mark Gross
This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifo…
The moduli space of (1,11)-polarized abelian surfaces is unirational
Mark Gross, Sorin Popescu
We prove that the moduli space A_{11}^{lev} of (1,11) polarized abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface: a^2b+b^2c+c^2d+…