2010
DOI: 10.4007/annals.2010.172.243
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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 … Show more

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Cited by 55 publications
(123 citation statements)
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“…This is the most studied case in the existing literature: Theorem 2.1 (Li-Ruan, 1997 [5] In fact the invariance for the total ancestror potential in all genera is established in [2] based on results in [3]. Recently the authors studied the problem for general ordinary flops without the "simple" assumption [4] and obtained, among other things, the invariance of quantum rings under the split assumptions of the bundles F and F .…”
Section: Ordinary Flopsmentioning
confidence: 99%
See 4 more Smart Citations
“…This is the most studied case in the existing literature: Theorem 2.1 (Li-Ruan, 1997 [5] In fact the invariance for the total ancestror potential in all genera is established in [2] based on results in [3]. Recently the authors studied the problem for general ordinary flops without the "simple" assumption [4] and obtained, among other things, the invariance of quantum rings under the split assumptions of the bundles F and F .…”
Section: Ordinary Flopsmentioning
confidence: 99%
“…The purpose is to introduce the results obtained by the authors in [3] and [4] and to work out a typical example.…”
Section: Gw Theorymentioning
confidence: 99%
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