<p>We study rank-two reflexive sheaves on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2025_451_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {P}^{3}}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2025_451_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">$c_2 =4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>, expanding on previous results for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2025_451_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">$c_2\le 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>≤</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. We show that every spectrum not previously ruled out is realized. Moreover, moduli spaces are studied and described in detail for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2025_451_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">$c_1=-1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> or 0 and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="574_2025_451_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">$c_3\ge 8$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>c</mi> <mn>3</mn> </msub> <mo>≥</mo> <mn>8</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

Rank-Two Reflexive Sheaves on the Projective Space with Second Chern Class Equal to Four

期刊论文
发表日期：

2025年5月4日

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Marcos Jardim,
Alan Muniz

摘要

We study rank-two reflexive sheaves on ${\mathbb {P}^{3}}$ $P^{3}$ with $c_2 =4$ $c_{2} = 4$ , expanding on previous results for $c_2\le 3$ $c_{2} \leq 3$ . We show that every spectrum not previously ruled out is realized. Moreover, moduli spaces are studied and described in detail for $c_1=-1$ $c_{1} = - 1$ or 0 and $c_3\ge 8$ $c_{3} \geq 8$ .