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Let us call a smooth projective vartiety $M$ as Calabi-Yau (CY) manifold if it has trivial canonical class and $h^i(M, \mathcal O_M ) = 0$ for $0 < i < \dim(M)$. In this definition, a CY 1-fold is an …

I am working on a suggestion of a comment here. Let $E \rightarrow \mathbb P^1$ be a non-trivial vector bundle of rank $r$ with $\deg E =0$ and $\mathbb P(E) \rightarrow \mathbb P^1$ be its projectiz …

I am doing some calculation on a toy example from the question here. Let $\mathbb P(E) \rightarrow \mathbb P^1$ be the projectization of the vector bundle $E = \mathcal O \oplus \mathcal O \oplus \ma …

Let $M$ be a connected projective complex manifold with a smooth anticanonical divisor $D$ ($D \sim -K_M$). In an answer to a previous question, It is told that $D$ may have at most two components. An …

Let's call a smooth projective vartiety $M$ as Calabi-Yau (CY) manifold if it has trivial canonical class and $h^i(M, \mathcal O_M ) = 0$ for $0 < i < \dim(M)$. In this definition, a CY 1-fold is an e …

We work over $\mathbb C$ and let us call a smooth projective vartiety $M$ as Calabi-Yau (CY) manifold if it has trivial canonical class and $h^i(M, \mathcal O_M ) = 0$ for $0 < i < \dim(M)$. In this d …

By a K3 fibered Calabi-Yau threefold, I mean a smooth projective threefold $X$ with trivial canonical class and $h^{1,0}(X) =h^{2,0}(X) = 0$ that has a fibration $X \rightarrow \mathbb P^1$ whose gen …