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Homotopy Theory Seminar

Friday, February 25, 2022 - 2:00pm to 3:00pm

Sabrina Pauli

Universität Duisburg-Essen


University of Pennsylvania

Clemens conjectured in 1984 that a general quintic threefold contains only a finite number of rational curves of a fixed degree d. This is true for d smaller or equal to 11, but still open for d>11. The number of degree d rational curves on a quintic threefold does not depend on the choice of quintic threefold when counting over an algebraically closed field, but this invariance breaks down for non-algebraically closed fields. Methods from A1-homotopy theory restore this invariance for arbitrary fields k when counting in the Witt ring W(k). In my talk I will explain how to use Marc Levine's quadratic version of Bott's residue formula to count rational curves of degree d in W(k) when d is less or equal to 3. This is based on joint work with Marc Levine.