All Questions

Pierre Deligne in his celebrated paper entitling "Local behavior of Hodge structures at infinity" introduced Maximal degenerations of Calabi-Yau manifolds. Let $\pi:X\to \mathbb C^*$ be a family of ...

"Motto" Moduli space of Calabi-Yau varieties can be connected by using Symplectic surgery theory. Miles Reid’s Fantasy:“There is only one Calabi-Yau space” i.e "All CY connected through conifold ...

Let $X$ be a Calabi–Yau threefold. Here, Calabi–Yau is understood to a mean a smooth simply connected projective threefold with $h^1(\mathcal{O}_X) = h^2(\mathcal{O}_X)=0$ and holomorphically trivial ...

Roughly, a toric degeneration is a proper flat family $f:\mathcal{X}\to D$ of relative dimension $n$ with the properties that $\mathcal{X}_t$ is an irreducible normal Calabi-Yau and $\mathcal{X}_0$ is ...

Let $X$ and $Y$ are Calabi-Yau varieties and mirror to each other. Then from HMS the Fukaya Floer category of Lagrangian intersections in $X$, is equivalent to bounded derived category of coherent ...

I am interested in understanding whether there are any significant connections between Calabi-Yau manifolds and number theory. Calabi-Yau manifolds are central objects in algebraic geometry and string ...