An example of birationally inequivalent projective symplectic varieties which are D-equivalent and L-equivalent


We give an example of a pair of projective symplectic varieties in arbitrarily large dimensions which are D-equivalent, L-equivalent, and birationally inequivalent.

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The author is indebted to Kota Yoshioka, Michal Kapustka, and Grzegorz Kapustka for pointing out a crucial error in Proposition 2.2 of the first draft and informing him of references. He is also greatful to Kota Yoshioka for sending the preprint version of [22] to the author, and to Atsushi Ito for pointing out a simplification in the proof of Proposition 2.2. The author was partially supported by Grants-in-Aid for Scientific Research (16H05994, 16K13746, 16H02141, 16K13743, 16K13755, 16H06337, 18H01120) and the Inamori Foundation.

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Correspondence to Shinnosuke Okawa.

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Okawa, S. An example of birationally inequivalent projective symplectic varieties which are D-equivalent and L-equivalent. Math. Z. 297, 459–464 (2021).

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