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Vladimir Baranovsky
Vladimir Baranovsky
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Let X be a projective variety (say, irreducible) and E a vector bundle on X or rank r. Is it true that there exists a codimension 2 closed subset Z in X such that restriction of E(n) (for n large enough) to U = X - Z has a trivial sub-bundle of rank (r-1)? Is this written somewhere? What happens when X varies in a flat family over a base S?

UPD: corrected the question - an ample twist of E is supposed to have a trivial sub-bundle.

Let X be a projective variety (say, irreducible) and E a vector bundle on X or rank r. Is it true that there exists a codimension 2 closed subset Z in X such that restriction of E to U = X - Z has a trivial sub-bundle of rank (r-1)? Is this written somewhere? What happens when X varies in a flat family over a base S?

Let X be a projective variety (say, irreducible) and E a vector bundle on X or rank r. Is it true that there exists a codimension 2 closed subset Z in X such that restriction of E(n) (for n large enough) to U = X - Z has a trivial sub-bundle of rank (r-1)? Is this written somewhere? What happens when X varies in a flat family over a base S?

UPD: corrected the question - an ample twist of E is supposed to have a trivial sub-bundle.

Source Link
Vladimir Baranovsky
Vladimir Baranovsky
  • 776
  • 3
  • 11

trivial subbundles

Let X be a projective variety (say, irreducible) and E a vector bundle on X or rank r. Is it true that there exists a codimension 2 closed subset Z in X such that restriction of E to U = X - Z has a trivial sub-bundle of rank (r-1)? Is this written somewhere? What happens when X varies in a flat family over a base S?