Irreducibility of the moduli space of orthogonal instanton bundles on P-n

Autor(es)

Andrade, Aline V. ^[1] ; Marchesi, Simone ^[2] ; Miro-Roig, Rosa M. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos UFSCAR, Dept Matemat, Rod Washington Luis, KM 235 CP 676, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Estadual Campinas UNICAMP, Inst Matemat Estat & Comp Cient, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[3] Univ Barcelona, Dept Matemat & Informat, Gran Via Corts Catalanes 585, E-08007 Barcelona - Spain

• Tipo de documento: Artigo Científico
• Fonte: REVISTA MATEMATICA COMPLUTENSE; v. 33, n. 1, p. 271-294, JAN 2020.
• Citações Web of Science: 0

Resumo

In order to obtain existence criteria for orthogonal instanton bundles on 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 P-n and prove that every orthogonal instanton bundle with no global sections on P-n and charge c >= 2 has rank r <=(n-1)c. We also prove that when the rank r of the bundles reaches the upper bound, M-Pn(O)(c,r), the coarse moduli space of orthogonal instanton bundles with no global sections on P-n, with charge c >= 2 and rank r, is affine, smooth, reduced and irreducible. Last, we construct Kronecker modules to determine the splitting type of the bundles in M-Pn(O)(c,r), whenever is non-empty. (AU)

• Processo FAPESP: 17/03487-9 - Fibrados vetoriais: da família instanton até uma nova regularidade
• Beneficiário: Simone Marchesi
• Modalidade de apoio: Auxílio à Pesquisa - Regular