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Let $Y_1$ and $Y_1'$ be index two degree one Fano threefolds. Suppose we have a Fourier-Mukai equivalence $\Phi_P : \mathrm{D}^b(Y_1) \to \mathrm{D}^b(Y_1')$. Can anything be said about the kernel $P$, i.e. is there some kind of a classification in this Fano case? Can we for example use Bondal-Orlov's theorem on the autoequivalences of $\mathrm{D}^b(Y_1)$, i.e. that $\mathrm{Aut}(\mathrm{D}^b(Y_1)) = \mathrm{Aut}(X) \ltimes (\mathrm{Pic}(X) \oplus \mathbb{Z})$, to say anything?

Thank you.

Let $Y_1$ and $Y_1'$ be index two degree one Fano threefolds. Suppose we have a Fourier-Mukai equivalence $\Phi_P : \mathrm{D}^b(Y_1) \to \mathrm{D}^b(Y_1')$. Can anything be said about the kernel $P$, i.e. is there some kind of a classification in this Fano case? Can we for example use Bondal-Orlov's theorem on the autoequivalences of $\mathrm{D}^b(Y_1)$, i.e. that $\mathrm{Aut}(\mathrm{D}^b(Y_1)) = \mathrm{Aut}(X) \ltimes (\mathrm{Pic}(X) \oplus \mathbb{Z})$, to say anything?

Thank you.

Let $Y_1$ and $Y_1'$ be index two degree one Fano threefolds. Suppose we have a Fourier-Mukai equivalence $\Phi_P : \mathrm{D}^b(Y_1) \to \mathrm{D}^b(Y_1')$. Can anything be said about the kernel $P$, i.e. is there some kind of a classification in this Fano case?

Thank you.

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mathphys
mathphys
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Let $Y_1$ and $Y_1'$ be index two degree one Fano threefolds. Suppose we have ana Fourier-Mukai equivalence $\Phi_P : \mathrm{D}^b(Y_1) \to \mathrm{D}^b(Y_1')$. Can anything be said about the kernel $P$, i.e. is there some kind of a classification in this Fano case? Can we for example use Bondal-Orlov's theorem on the autoequivalences of $\mathrm{D}^b(Y_1)$, i.e. that $\mathrm{Aut}(\mathrm{D}^b(Y_1)) = \mathrm{Aut}(X) \ltimes (\mathrm{Pic}(X) \oplus \mathbb{Z})$, to say anything?

Thank you.

Let $Y_1$ and $Y_1'$ be index two degree one Fano threefolds. Suppose we have an Fourier-Mukai equivalence $\Phi_P : \mathrm{D}^b(Y_1) \to \mathrm{D}^b(Y_1')$. Can anything be said about the kernel $P$, i.e. is there some kind of a classification in this Fano case? Thank you.

Let $Y_1$ and $Y_1'$ be index two degree one Fano threefolds. Suppose we have a Fourier-Mukai equivalence $\Phi_P : \mathrm{D}^b(Y_1) \to \mathrm{D}^b(Y_1')$. Can anything be said about the kernel $P$, i.e. is there some kind of a classification in this Fano case? Can we for example use Bondal-Orlov's theorem on the autoequivalences of $\mathrm{D}^b(Y_1)$, i.e. that $\mathrm{Aut}(\mathrm{D}^b(Y_1)) = \mathrm{Aut}(X) \ltimes (\mathrm{Pic}(X) \oplus \mathbb{Z})$, to say anything?

Thank you.

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mathphys
mathphys
  • 305
  • 1
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Fourier-Mukai kernels for Fano threefolds

Let $Y_1$ and $Y_1'$ be index two degree one Fano threefolds. Suppose we have an Fourier-Mukai equivalence $\Phi_P : \mathrm{D}^b(Y_1) \to \mathrm{D}^b(Y_1')$. Can anything be said about the kernel $P$, i.e. is there some kind of a classification in this Fano case? Thank you.