An invitation to the fiber-full scheme

Abstract: I will 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 particular, given a sequence of functions $(h_0,..,h_n)$ the fiber-full scheme parameterizes subschemes $X$ of $P^n$ satisfying dim $H^i(X,O_X(v)) = h_i(v).$ In this talk I will sketch the construction of the fiber-full scheme and describe some examples associated with classical Hilbert schemes. I will also discuss various future directions one can pursue. This is joint work with Yairon-Cid Ruiz. Chairperson - N. Mohan Kumar

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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