The Franchetta conjecture for vector bundles.

Duration: 1 hour 2 mins

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Description:	Ravindra Girivaru University of Missouri 10 May 2022 – 16:00 to 17:00


Created:	2022-06-01 08:51
Collection:	K-theory, algebraic cycles and motivic homotopy theory
Publisher:	Isaac Newton Institute
Copyright:	Ravindra Girivaru
Language:	eng (English)


Abstract:	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.

Abstract:

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.

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