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Yaniv Ganor
Yaniv Ganor
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I am reading a paper and there is some computation of RHom of sheaves that I don't understand. I hope this is the right place to ask. It is this paper, example 3.10 , page 25 arxiv.org/pdf/1005.1517v4.pdf In the first RHom equality there, They claim that:

$R\mathcal{Hom}(k_{\Delta\times\{0\}}, k_{M\times M\times \mathbb R}) = k_{\Delta\times\{0\}}[-n-1]$$R\mathcal{Hom}(k_{\Delta\times\{0\}}, k_{M\times M\times \mathbb R}) \simeq k_{\Delta\times\{0\}}[-n-1]$

Where, for a closed immersion $j: N\to M$ of manifolds we denote by $k_N := j_*j^{-1}k_M$ where $k_M$ is the constant sheaf on $M$, and the diagonal of $M\times M$ is denoted by $\Delta$.

Why does the result come shifted by the codimension? How does one begin to compute RHoms of such sheaves in general? will deRahm resolution work?

Thanks !

I am reading a paper and there is some computation of RHom of sheaves that I don't understand. I hope this is the right place to ask. It is this paper, example 3.10 , page 25 arxiv.org/pdf/1005.1517v4.pdf In the first RHom equality there, They claim that:

$R\mathcal{Hom}(k_{\Delta\times\{0\}}, k_{M\times M\times \mathbb R}) = k_{\Delta\times\{0\}}[-n-1]$

Where, for a closed immersion $j: N\to M$ of manifolds we denote by $k_N := j_*j^{-1}k_M$ where $k_M$ is the constant sheaf on $M$, and the diagonal of $M\times M$ is denoted by $\Delta$.

Why does the result come shifted by the codimension? How does one begin to compute RHoms of such sheaves in general? will deRahm resolution work?

Thanks !

I am reading a paper and there is some computation of RHom of sheaves that I don't understand. I hope this is the right place to ask. It is this paper, example 3.10 , page 25 arxiv.org/pdf/1005.1517v4.pdf In the first RHom equality there, They claim that:

$R\mathcal{Hom}(k_{\Delta\times\{0\}}, k_{M\times M\times \mathbb R}) \simeq k_{\Delta\times\{0\}}[-n-1]$

Where, for a closed immersion $j: N\to M$ of manifolds we denote by $k_N := j_*j^{-1}k_M$ where $k_M$ is the constant sheaf on $M$, and the diagonal of $M\times M$ is denoted by $\Delta$.

Why does the result come shifted by the codimension? How does one begin to compute RHoms of such sheaves in general? will deRahm resolution work?

Thanks !

Copied formulas from paper into the question text
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Yaniv Ganor
Yaniv Ganor
  • 1.9k
  • 1
  • 18
  • 29

I am reading a paper and there is some computation of RHom of sheaves that I don't understand. I hope this is the right place to ask. It is this paper, example 3.10 , page 25 arxiv.org/pdf/1005.1517v4.pdfarxiv.org/pdf/1005.1517v4.pdf TheIn the first RHom equality. Why does the result come shifted there, They claim that:

$R\mathcal{Hom}(k_{\Delta\times\{0\}}, k_{M\times M\times \mathbb R}) = k_{\Delta\times\{0\}}[-n-1]$

Where, for a closed immersion $j: N\to M$ of manifolds we denote by the codimension? (In$k_N := j_*j^{-1}k_M$ where $k_M$ is the paper they denoteconstant sheaf on $M$, and the diagonal of $M\times M$ is denoted by $\Delta$.)

Why does the result come shifted by the codimension? How does one begin to compute RHoms of such sheaves in general? will deRahm resolution work?

Thanks !

I am reading a paper and there is some computation of RHom of sheaves that I don't understand. I hope this is the right place to ask. It is this paper, example 3.10 , page 25 arxiv.org/pdf/1005.1517v4.pdf The first RHom equality. Why does the result come shifted by the codimension? (In the paper they denote the diagonal of $M\times M$ by $\Delta$.) How does one begin to compute RHoms of such sheaves in general? will deRahm resolution work?

Thanks !

I am reading a paper and there is some computation of RHom of sheaves that I don't understand. I hope this is the right place to ask. It is this paper, example 3.10 , page 25 arxiv.org/pdf/1005.1517v4.pdf In the first RHom equality there, They claim that:

$R\mathcal{Hom}(k_{\Delta\times\{0\}}, k_{M\times M\times \mathbb R}) = k_{\Delta\times\{0\}}[-n-1]$

Where, for a closed immersion $j: N\to M$ of manifolds we denote by $k_N := j_*j^{-1}k_M$ where $k_M$ is the constant sheaf on $M$, and the diagonal of $M\times M$ is denoted by $\Delta$.

Why does the result come shifted by the codimension? How does one begin to compute RHoms of such sheaves in general? will deRahm resolution work?

Thanks !

Source Link
Yaniv Ganor
Yaniv Ganor
  • 1.9k
  • 1
  • 18
  • 29

Help understand a calculation involving RHom of sheaves on manifolds

I am reading a paper and there is some computation of RHom of sheaves that I don't understand. I hope this is the right place to ask. It is this paper, example 3.10 , page 25 arxiv.org/pdf/1005.1517v4.pdf The first RHom equality. Why does the result come shifted by the codimension? (In the paper they denote the diagonal of $M\times M$ by $\Delta$.) How does one begin to compute RHoms of such sheaves in general? will deRahm resolution work?

Thanks !