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Bin Wang
Bin Wang
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I know the definition of the ring of differential operators, by using the smooth coverings. But I do not know how to calculate the global section.

Can anyone help explain that why the global section of twisted differential operators on $Bun_{G}$ are locally constant functions except when it is twisted by $\omega^{1/2}$?

Here $Bun_{G}$ is the moduli stack of $G$-bundles on a smooth algebraic curve $X$ over $\mathbb{C}$, $G$ is semisimple. $\omega$ is the canonical line bundle. I do not know whether this is true for other algebraically closed field

I know the definition of the ring of differential operators, by using the smooth coverings. But I do not know how to calculate the global section.

Can anyone help explain that why the global section of twisted differential operators on $Bun_{G}$ are constant except twisted by $\omega^{1/2}$?

Here $Bun_{G}$ is the moduli stack of $G$-bundles on a smooth algebraic curve $X$ over $\mathbb{C}$, $G$ is semisimple. $\omega$ is the canonical line bundle. I do not know whether this is true for other algebraically closed field

I know the definition of the ring of differential operators, by using the smooth coverings. But I do not know how to calculate the global section.

Can anyone help explain that why the global section of twisted differential operators on $Bun_{G}$ are locally constant functions except when it is twisted by $\omega^{1/2}$?

Here $Bun_{G}$ is the moduli stack of $G$-bundles on a smooth algebraic curve $X$ over $\mathbb{C}$, $G$ is semisimple. $\omega$ is the canonical line bundle. I do not know whether this is true for other algebraically closed field

added 31 characters in body
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Bin Wang
Bin Wang
  • 193
  • 8

I know the definition of the ring of differential operators, by using the smooth coveringcoverings. But I do not know how to calculate the global section.

Can anyone help explain that why the global section of twisted differential operators on $Bun_{G}$ are constant except twisted by $\omega_{X}^{1/2}$$\omega^{1/2}$?

Here $Bun_{G}$ is the moduli stack of $G$-bundles on a smooth algebraic curve $X$ over $\mathbb{C}$, here $G$ is semisimple. $\omega$ is the canonical line bundle. I do not know whether this is true for other algebraically closed field

I know the definition of the ring of differential operators, by using the smooth covering. But I do not know how to calculate the global section.

Can anyone help explain that why the global section of twisted differential operators on $Bun_{G}$ are constant except twisted by $\omega_{X}^{1/2}$?

Here $Bun_{G}$ is the moduli stack of $G$-bundles on a smooth algebraic curve $X$ over $\mathbb{C}$, here $G$ is semisimple. I do not know whether this is true for other algebraically closed field

I know the definition of the ring of differential operators, by using the smooth coverings. But I do not know how to calculate the global section.

Can anyone help explain that why the global section of twisted differential operators on $Bun_{G}$ are constant except twisted by $\omega^{1/2}$?

Here $Bun_{G}$ is the moduli stack of $G$-bundles on a smooth algebraic curve $X$ over $\mathbb{C}$, $G$ is semisimple. $\omega$ is the canonical line bundle. I do not know whether this is true for other algebraically closed field

Source Link
Bin Wang
Bin Wang
  • 193
  • 8

Global section of differential operators on moduli stack of G bundles

I know the definition of the ring of differential operators, by using the smooth covering. But I do not know how to calculate the global section.

Can anyone help explain that why the global section of twisted differential operators on $Bun_{G}$ are constant except twisted by $\omega_{X}^{1/2}$?

Here $Bun_{G}$ is the moduli stack of $G$-bundles on a smooth algebraic curve $X$ over $\mathbb{C}$, here $G$ is semisimple. I do not know whether this is true for other algebraically closed field