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math.AG2024
Complex Bott Periodicity in algebraic geometry
Hannah Larson, Ravi Vakil
We state and prove a form of Bott periodicity (for ) in an algebraic setting (so, ) which makes sense over , which also specializes to Bott periodicity in…
math.AG2024
Tschirnhausen bundles of covers of the projective line
Ravi Vakil, Sameera Vemulapalli
A degree genus cover of the complex projective line by a smooth curve yields a vector bundle on the projective line by pushforward of the structure sheaf. Which bundles…
math.AG2024
The interpolation problem: When can you pass a curve of a given type through N random points in space?
Eric Larson, Ravi Vakil, Isabel Vogt
The interpolation problem is a natural and fundamental question whose roots trace back to ancient Greece. The story is long and rich, with many chapters, and a complete solution ha…