We study the irreducible components of the moduli space of instanton sheaveson $\mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with$c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In particular, weclassify all instanton sheaves with $c_2(E)\le4$, describing all theirreducible components of their moduli space. A key ingredient for our argumentis the study of the moduli space ${\mathcal T}(d)$ of stable sheaves on$\mathbb{P}^3$ with Hilbert polynomial $P(t)=d\cdot t$, which contains, as anopen subset, the moduli space of rank 0 instanton sheaves of multiplicity $d$;we describe all the irreducible components of ${\mathcal T}(d)$ for $d\le4$.
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机译:我们研究了瞬时子sheaveson $ \ mathbb {P} ^ 3 $的模空间的不可约成分,即满足$ h ^的秩为2的无扭力滑轮$ E $,其中$ c_1(E)= c_3(E)= 0 $ 1(E(-2))= h ^ 2(E(-2))= 0 $。特别是,我们用$ c_2(E)\ le4 $对所有瞬时槽轮进行分类,描述其模量空间的所有可归约分量。我们论证的关键要素是研究希尔伯特多项式$ P(t)= d \ cdot t $时,稳定在$ \ mathbb {P} ^ 3 $上的滑轮的模空间$ {\ mathcal T}(d)$,其中包含作为开放子集的多重度为$ d $的第0级瞬时量槽的模空间;我们以$ d \ le4 $描述了$ {\ mathcal T}(d)$的所有不可约分量。
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