Endomorphisms of varieties
Endomorphisms of varieties
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Burt Totaro, UCLA and IAS
A natural class of dynamical systems is obtained by iterating听polynomial maps, which can be viewed as maps from projective space to听itself. One can ask which other projective varieties admit endomorphisms听of degree greater than 1. This seems to be an extremely restrictive听property, with all known examples coming from toric varieties (such as听projective space) or abelian varieties. We describe what is known in听this direction, with the new ingredient being the "Bott vanishing"听property.
Joint work with Tatsuro Kawakami.