Flops, motives, and invariance of quantum rings

Abstract

For ordinary flops, the correspondence defined by the graph closure is shown to give equivalence of Chow motives and to preserve the Poincaré pairing. In the case of simple ordinary flops, this correspondence preserves the big quantum cohomology ring after an analytic continuation over the extended Kähler moduli space.

For Mukai flops, it is shown that the birational map for the local models is deformation equivalent to isomorphisms. This implies that the birational map induces isomorphisms on the full quantum theory and all the quantum corrections attached to the extremal ray vanish.

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Authors

Yuan-Pin Lee

Department of Mathematics
University of Utah
Salt Lake City, Utah 84103
United States

Hui-Wen Lin

Department of Mathematics
National Taiwan University
No. 1, Sec. 4, Roosevelt Road
Taipei, 10617
Taiwan
and
Department of Mathematics
National Central University
Chung-Li
Taiwan

Chin-Lung Wang

Department of Mathematics
National Taiwan University
No. 1, Sec. 4, Roosevelt Road
Taipei, 10617
Taiwan
and
Department of Mathematics
National Central University
Chung-Li
Taiwan