Let H be a subgroup of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_837_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathop {\textrm{PGL}}\limits (2,\mathbb {C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>PGL</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> (respectively, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_837_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">$\textrm{SL}(2,\mathbb {C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SL</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>) such that the Zariski closure in <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_837_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathop {\textrm{PGL}}\limits (2,\mathbb {C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>PGL</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> (respectively, <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_837_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">$\textrm{SL}(2,\mathbb {C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SL</mtext> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>) of some compact subgroup of H contains H. We classify the H-equivariant holomorphic vector bundles on <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_837_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb{C}\mathbb{P}^1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">C</mi> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mn>1</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. This generalizes [<CitationRef CitationID="CR1">1</CitationRef>], where H was assumed to be a finite abelian group.

On the equivariant vector bundles on $\pmb {\mathbb{C}\mathbb{P}^1}$

期刊论文
发表日期：

2025年8月27日

查看全文

Indranil Biswas,
Manish Kumar,
A J Parameswaran

摘要

Let H be a subgroup of $\mathop {\textrm{PGL}}\limits (2,\mathbb {C})$ $PGL (2, C)$ (respectively, $\textrm{SL}(2,\mathbb {C})$ $SL (2, C)$ ) such that the Zariski closure in $\mathop {\textrm{PGL}}\limits (2,\mathbb {C})$ $PGL (2, C)$ (respectively, $\textrm{SL}(2,\mathbb {C})$ $SL (2, C)$ ) of some compact subgroup of H contains H. We classify the H-equivariant holomorphic vector bundles on $\mathbb{C}\mathbb{P}^1$ $C P^{1}$ . This generalizes [1], where H was assumed to be a finite abelian group.

On the equivariant vector bundles on \(\pmb {\mathbb{C}\mathbb{P}^1}\)

摘要