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Thanks for fixing the typo/format error I introduced in the title. I think I've now got the en dashes to work; fixed a hyphen in the main text
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Yemon Choi
Yemon Choi
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$G$-equivariant coherent sheaves on BottBott$-Samelson Resolutions$Samelson resolutions

Let $G$ be a Lie group and $B$ a Borel subgroup. $G/B$ is the corresponding flag variety.

Let $w$ be an element of the Weyl group $W$ with a reduced expression $w = s_1 \cdots s_n$. Let $X_w$ be the corresponding Schubert variety in the flag variety, and $BS(s_1,...s_n)$ the corresponding Bott-SamelsonBott–Samelson resolution.

There is a birational map $$f: BS(s_1,s_2,...,s_n) \rightarrow X_{s_1s_2...s_n} \subset G/B$$$$f: BS(s_1,s_2,...,s_n) \rightarrow X_{s_1s_2...s_n} \subset G/B\,.$$.

What can we say about the (derived) pushforward of the structure sheaf $\mathcal{O}$ on $BS(s_1,s_2,...,s_n)$?

Is that the convolution product of some $G-$$G$-equivariant coherent sheaves on $X_w \subset G/B$?

$G$-equivariant coherent sheaves on Bott-Samelson Resolutions

Let $G$ be a Lie group and $B$ a Borel subgroup. $G/B$ is the corresponding flag variety.

Let $w$ be an element of the Weyl group $W$ with a reduced expression $w = s_1 \cdots s_n$. Let $X_w$ be the corresponding Schubert variety in the flag variety, and $BS(s_1,...s_n)$ the corresponding Bott-Samelson resolution.

There is a birational map $$f: BS(s_1,s_2,...,s_n) \rightarrow X_{s_1s_2...s_n} \subset G/B$$.

What can we say about the (derived) pushforward of the structure sheaf $\mathcal{O}$ on $BS(s_1,s_2,...,s_n)$?

Is that the convolution product of some $G-$equivariant coherent sheaves on $X_w \subset G/B$?

$G$-equivariant coherent sheaves on Bott$-$Samelson resolutions

Let $G$ be a Lie group and $B$ a Borel subgroup. $G/B$ is the corresponding flag variety.

Let $w$ be an element of the Weyl group $W$ with a reduced expression $w = s_1 \cdots s_n$. Let $X_w$ be the corresponding Schubert variety in the flag variety, and $BS(s_1,...s_n)$ the corresponding Bott–Samelson resolution.

There is a birational map $$f: BS(s_1,s_2,...,s_n) \rightarrow X_{s_1s_2...s_n} \subset G/B\,.$$.

What can we say about the (derived) pushforward of the structure sheaf $\mathcal{O}$ on $BS(s_1,s_2,...,s_n)$?

Is that the convolution product of some $G$-equivariant coherent sheaves on $X_w \subset G/B$?

fixed a typo in title
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edit approved Jun 2, 2016 at 0:22
Sean Lawton
edit approved Jun 2, 2016 at 0:22
Sean Lawton
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$G$-equivariant coherent sheaves on Bott–SamelsonBott-Samelson Resolutions

En dashes not hypens, IIRC from my sub-editing days. Also tweaked some of the "soit" phrases
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Yemon Choi
Yemon Choi
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$G$-equivariant coherent sheaves on Bott-SamelsonBott–Samelson Resolutions

Let $G$ be a Lie group, and $B$ be a Borel subgroup. $G/B$ is the corresponding flag variety.

Let $w$ be an element of the Weyl group $W$ with a reduced expression $w = s_1 \cdots s_n$. Let $X_w$ be the corresponding Schubert variety in the flag variety, and $BS(s_1,...s_n)$ be the corresponding Bott-Samelson resolution.

There is a birational map $$f: BS(s_1,s_2,...,s_n) \rightarrow X_{s_1s_2...s_n} \subset G/B$$.

What can we say about the (derived) pushforward of the structure sheaf $\mathcal{O}$ on $BS(s_1,s_2,...,s_n)$?

Is that the convolution product of some $G-$equivariant coherent sheaves on $X_w \subset G/B$?

$G$-equivariant coherent sheaves on Bott-Samelson Resolutions

Let $G$ be a Lie group, $B$ be a Borel subgroup. $G/B$ is the corresponding flag variety.

Let $w$ be an element of the Weyl group $W$ with a reduced expression $w = s_1 \cdots s_n$. Let $X_w$ be the corresponding Schubert variety in the flag variety, and $BS(s_1,...s_n)$ be the corresponding Bott-Samelson resolution.

There is a birational map $$f: BS(s_1,s_2,...,s_n) \rightarrow X_{s_1s_2...s_n} \subset G/B$$.

What can we say about the (derived) pushforward of the structure sheaf $\mathcal{O}$ on $BS(s_1,s_2,...,s_n)$?

Is that the convolution product of some $G-$equivariant coherent sheaves on $X_w \subset G/B$?

$G$-equivariant coherent sheaves on Bott–Samelson Resolutions

Let $G$ be a Lie group and $B$ a Borel subgroup. $G/B$ is the corresponding flag variety.

Let $w$ be an element of the Weyl group $W$ with a reduced expression $w = s_1 \cdots s_n$. Let $X_w$ be the corresponding Schubert variety in the flag variety, and $BS(s_1,...s_n)$ the corresponding Bott-Samelson resolution.

There is a birational map $$f: BS(s_1,s_2,...,s_n) \rightarrow X_{s_1s_2...s_n} \subset G/B$$.

What can we say about the (derived) pushforward of the structure sheaf $\mathcal{O}$ on $BS(s_1,s_2,...,s_n)$?

Is that the convolution product of some $G-$equivariant coherent sheaves on $X_w \subset G/B$?

minor formatting edits, fixed uncompiled TeX in title.
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edit approved May 30, 2016 at 14:57
Sean Lawton
edit approved May 30, 2016 at 14:57
Sean Lawton
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Qiao
Qiao
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