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Abstract
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Consider a projective variety X and its automorphism group, Aut(X). It is known that the connected component of the identity in Aut(X) is an algebraic group, Aut^o(X). In this talk, we will show that any connected algebraic group is isomorphic to Aut^o(X) for some projective variety X. In contrast, we will see that the algebraic semigroups of endomorphisms of X have a very restricted structure.
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