The flips-flops tag has no usage guidance.

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### Grassmannian inside a hyperkahler manifold

I am currently looking at stratified Mukai flop. Roughly speaking, this is a construction that, starting with a grassmannian $G$ inside a hyperkahler $X$ produces a birational manifold $X^*$ (with a ...

**4**

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### $Ex(f)$ has codimension at least 2

The following is a part of proof of lemma 6.2 in the book.
$f:X \to Y$ a projective birational morphism of normal varieties
$D$: Weil divisor on $Y$, $E$: exceptional divisor of $f$
$\mathcal{O}_X(...

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**1**answer

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### Is the number of minimal models finite

Let $X$ be a variety of general type.
Assume that $\dim X = 3$. In https://eudml.org/doc/164223 it is proven that $X$ has only finitely many minimal models (i.e., only $\mathbb Q$-factorial terminal ...

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### Recognizing a Mukai flop

Let us first review the usual construction of a Mukai flop. Suppose $M$ is a smooth $2m$-dimensional projective variety over $\mathbb C$ containing a closed $m$-dimensional subvariety $W$, and suppose ...

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### Why is the standard flop a flop?

I have seen at least two ways to define flops (and similarly flips).
We start with $Y \to X$, a surjective birational morphism, contracting a locus of codimension at least 2, such that $K_Y$ is ...

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### Is a flop on Calabi-Yau threefolds always Atiyah flop?

Is it true that any flop on a Calabi-Yau threefold is given by the Atiyah flop? That is, there always exists a rigid rational curve $\mathbb{P}^1$ with normal bundle $\mathcal{O}_{\mathbb{P}^1}(-1)^{\...

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### What is the Exceptional Locus of a flopping contraction between threefolds?

Hi,
I'm trying to understand the group of cycles (modulo numerical equivalence) contracted by a flopping contraction $f$.
More precisely, I'm in the setup of Definition 2.12 of this paper by ...