Fellowship Of The Ring: The Fiber-Full Scheme
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We introduce the fiber-full scheme which can be seen as the parameter space that generalizes the Hilbert and Quot schemes by controlling the entire cohomological data. In other words, the fiber-full scheme controls the dimension of all cohomologies of all possible twistings, instead of just the Hilbert polynomial. We also present some applications that can be derived from the existence of the fiber-full scheme. This talk is based on joint work with Ritvik Ramkumar.
The Fiber-Full Scheme