Complete Intersections with S^1-action

Abstract

We give the diffeomorphism classification of complete intersections with S^1-symmetry in dimension less than or equal to 6. In particular, we show that a 6-dimensional complete intersection admits a smooth non-trivial S^1-action if and only if it is diffeomorphic to the complex projective space or the quadric. We also prove that in any odd complex dimension only finitely many complete intersections can carry a smooth effective action by a torus of rank $>1$.

arXiv commentupdated, revised and extended version including a finiteness result for complete intersections with torus actions of rank 2, v5: minor modifications, v6: reference updated, final version, to appear in Transformation Groups

References in corpus (3)

• A note on torus actions and the Witten genus
• Dirac-operators and symmetries of quasitoric manifolds
• Bordism-finiteness and semi-simple group actions

Cited by in corpus (3)

• A note on torus actions and the Witten genus
• Elliptic genera of level $N$ for complete intersections
• Hamiltonian $S^1$-actions on complete intersections