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The Franchetta conjecture for vector bundles.

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

The original Franchetta theorem/conjecture for line bundles says that the restriction of any line bundle on the universal family of genus g curves for g at least 2 to any smooth curve in the family is a power of the canonical bundle. This conjecture was later generalized by O’Grady for Chow groups of 0-cycles on families of K3 surfaces. I will talk about an analogue of this conjecture for higher rank bundles on hypersurfaces in projective space and how this relates to Noether-Lefschetz theory.

This talk is part of the Isaac Newton Institute Seminar Series series.

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