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New families of rank 2 bundles on projective space

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 نشر من قبل Marcos Jardim
 تاريخ النشر 2016
  مجال البحث
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We present a new family of monads whose cohomology is a stable rank two vector bundle on $PP$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. Such facts are used to prove that the moduli space of stable rank two vector bundles of zero first Chern class and second Chern class equal to 5 has exactly three irreducible components.

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We present a new family of monads whose cohomology is a stable rank two vector bundle on $mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used to constru ct a new infinite series of rational moduli components of stable rank two vector bundles with trivial determinant and growing second Chern class. We also prove that the moduli space of stable rank two vector bundles with trivial determinant and second Chern class equal to 5 has exactly three irreducible rational components.
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