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Let $X \subset \mathbb{P}^5$ be a rationalPfaffian cubic fourfold (e.g. a Pfaffianor one of the other known rational cubic fourfoldfourfolds). It is known by Kuznetsov's Homological Projective Duality that $\mathcal{K}u(X) \simeq D^b(S)$ where $\mathcal{K}u(X)$ is the Kuznetsov component of $D^b(X)$, and $S$ is a K3 surface.

What is the explicit definition of the functor $\Phi \colon \mathcal{K}u(X) \xrightarrow{\sim} D^b(S)$?

Let $X \subset \mathbb{P}^5$ be a rational cubic fourfold (e.g. a Pfaffian cubic fourfold). It is known by Kuznetsov's Homological Projective Duality that $\mathcal{K}u(X) \simeq D^b(S)$ where $\mathcal{K}u(X)$ is the Kuznetsov component of $D^b(X)$, and $S$ is a K3 surface.

What is the explicit definition of the functor $\Phi \colon \mathcal{K}u(X) \xrightarrow{\sim} D^b(S)$?

Let $X \subset \mathbb{P}^5$ be a Pfaffian cubic fourfold (or one of the other known rational cubic fourfolds). It is known by Kuznetsov's Homological Projective Duality that $\mathcal{K}u(X) \simeq D^b(S)$ where $\mathcal{K}u(X)$ is the Kuznetsov component of $D^b(X)$, and $S$ is a K3 surface.

What is the explicit definition of the functor $\Phi \colon \mathcal{K}u(X) \xrightarrow{\sim} D^b(S)$?

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mathphys
mathphys
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Let $X \subset \mathbb{P}^5$ be a rational cubic fourfold (e.g. a Pfaffian cubic fourfold). It is known by Kuznetsov's Homological Projective Duality that $\mathcal{K}u(X) \simeq D^b(S)$ where $\mathcal{K}u(X)$ is the Kuznetsov component of $D^b(X)$, and $S$ is a K3 surface.

What is the explicit definition of the functor $\Phi \colon \mathcal{K}u(X) \to D^b(S)$$\Phi \colon \mathcal{K}u(X) \xrightarrow{\sim} D^b(S)$?

Let $X \subset \mathbb{P}^5$ be a rational cubic fourfold (e.g. a Pfaffian cubic fourfold). It is known by Kuznetsov's Homological Projective Duality that $\mathcal{K}u(X) \simeq D^b(S)$ where $\mathcal{K}u(X)$ is the Kuznetsov component of $D^b(X)$, and $S$ is a K3 surface.

What is the explicit definition of the functor $\Phi \colon \mathcal{K}u(X) \to D^b(S)$?

Let $X \subset \mathbb{P}^5$ be a rational cubic fourfold (e.g. a Pfaffian cubic fourfold). It is known by Kuznetsov's Homological Projective Duality that $\mathcal{K}u(X) \simeq D^b(S)$ where $\mathcal{K}u(X)$ is the Kuznetsov component of $D^b(X)$, and $S$ is a K3 surface.

What is the explicit definition of the functor $\Phi \colon \mathcal{K}u(X) \xrightarrow{\sim} D^b(S)$?

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mathphys
mathphys
  • 305
  • 1
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Explicit functor from Kuznetsov component to derived category of K3 for rational cubic fourfolds

Let $X \subset \mathbb{P}^5$ be a rational cubic fourfold (e.g. a Pfaffian cubic fourfold). It is known by Kuznetsov's Homological Projective Duality that $\mathcal{K}u(X) \simeq D^b(S)$ where $\mathcal{K}u(X)$ is the Kuznetsov component of $D^b(X)$, and $S$ is a K3 surface.

What is the explicit definition of the functor $\Phi \colon \mathcal{K}u(X) \to D^b(S)$?