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ON TOPOLOGICAL PROPERTIES OF POSITIVE COMPLEXITY ONE SPACES

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Abstract

Motivated by work of Fine and Panov, and of Lindsay and Panov, we prove that every closed symplectic complexity one space that is positive (e.g., positive monotone) enjoys topological properties that Fano varieties with a complexity one holomorphic torus action possess. In particular, such spaces are simply connected, have Todd genus equal to one and vanishing odd Betti numbers.

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Correspondence to D. SEPE.

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S. Sabatini is partially supported by Deutsche Forschungsgemeinschaft.

D. Sepe is partially supported by Deutsche Forschungsgemeinschaft, CNPq and CAPES.

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SABATINI, S., SEPE, D. ON TOPOLOGICAL PROPERTIES OF POSITIVE COMPLEXITY ONE SPACES. Transformation Groups 27, 723–735 (2022). https://doi.org/10.1007/s00031-020-09588-y

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