patrick D Baier in his PhD thesis in chapter2 in page 14 for proving the theorem 2.1.4 used of following non-trivial fact Let $0\neq X\in V $(here $V$ is of dimension 6) , $W^*=A …

I would like to know for which Calabi-Yau threefolds SYZ conjecture is known to hold. I am aware of works by Gross-Wilson (Borcea-Voisin CY3s) and Ruan (quintic CY3), but they are …

I remember some talks some time ago about proofs of nonexistence of Lagrangian Kleinian bottles in C^2 for the standard symplectic structure, mentioning that this were the only com …

Is the following statement well known? Let $M,N$ be symplectic (algebraic) manifolds. Let $L \subset M \times N$ be a (smooth) Lagrangian correspondence. For a subset $X \subset M …

Hi all, I want to ask something about the holomorphic sections on elliptic K3: Is there any obstruction for an ellptic K3 (as an elliptic fibration) to have holomorphic sections? …

Suppose I have a symplectic manifold $M$, and have a deformation quantization of it, i.e. an associative product $\ast:C(M)[[\hbar]]\otimes C(M)[[\hbar]]\to C(M)[[\hbar]]$ so that …

Let p:X \to Y be a map of smooth algebraic varieties. Let $C \subset T^* X$ be a (locally closed) submanifold. Denote by $p_*(C) \subset T^* Y$ the following set: $\ \ \ \ \ \ …

Is the following fact well known? Let $X$ be a manifold and $V$ be a vector space. Let $E_1$ be a sub-bundle of the constant bundle $X \times V$. Let $E_2$ be its orthogonal c …

Suppose I have a symplectic manifold $(M,\omega)$ and a line bundle $\mathcal L$ with a connection with curvature $\omega$ (or perhaps it's more standard to say $\frac i{2\pi}\omeg …

This is a bit of a stab in the dark but I was wondering if anyone has defined cohomology classes on a hyperkähler manifold which pull back to the Stiefel-Whitney classes on any sub …