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Irreducibility of the moduli space of orthogonal instanton bundles on $$\mathbb {P}^n$$Pn
Revista Matemática Complutense ( IF 0.8 ) Pub Date : 2019-07-29 , DOI: 10.1007/s13163-019-00317-y
Aline V. Andrade , Simone Marchesi , Rosa M. Miró-Roig

In order to obtain existence criteria for orthogonal instanton bundles on \(\mathbb {P}^n\), we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such correspondence we are able to provide explicit examples of orthogonal instanton bundles with no global sections on \(\mathbb {P}^n\) and prove that every orthogonal instanton bundle with no global sections on \(\mathbb {P}^n\) and charge \(c\ge 2\) has rank \(r \le (n-1)c\). We also prove that when the rank r of the bundles reaches the upper bound, \(\mathcal {M}_{\mathbb {P}^n}^{\mathcal {O}}(c,r)\), the coarse moduli space of orthogonal instanton bundles with no global sections on \(\mathbb {P}^n\), with charge \(c\ge 2\) and rank r, is affine, smooth, reduced and irreducible. Last, we construct Kronecker modules to determine the splitting type of the bundles in \(\mathcal {M}_{\mathbb {P}^n}^{\mathcal {O}}(c,r)\), whenever is non-empty.

中文翻译:

$$ \ mathbb {P} ^ n $$ Pn上正交瞬时子束的模空间的不可约性

为了获得\(\ mathbb {P} ^ n \)上正交瞬时子束的存在准则,我们在没有全局截面和对称形式的正交瞬时子束的等价类之间提供了双射。使用这种对应关系,我们能够提供在\(\ mathbb {P} ^ n \)上没有全局截面的正交瞬时子束的显式示例,并证明在\(\ mathbb {P} ^ n \)和电荷\ {c \ ge 2 \)具有等级\ {r \ le(n-1)c \)。我们还证明,当束的秩r达到上限时,\(\ mathcal {M} _ {\ mathbb {P} ^ n} ^ {\ mathcal {O}}(c,r)\),在\(\ mathbb {P} ^ n \)上没有全局截面,电荷为\(c \ ge 2 \)和秩为r的正交瞬时子束的粗糙模空间是仿射,平稳,约简和不可约的。最后,我们构造Kronecker模块以确定\(\ mathcal {M} _ {\ mathbb {P} ^ n} ^ {\ mathcal {O}}(c,r)\)中束的分裂类型,只要非空。
更新日期:2019-07-29
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