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A quantum connection approach to rationality
Luiz Carazolli, Leonardo F. Cavenaghi, Ludmil Katzarkov, Maxim Kontsevich, Pedro Antonio Muniz Martins
Source abstract
We extract rank and regularized exponents from cyclic generic factors of the quantum connection and show that these data persist under the birational comparisons considered here. Applications include showing non-rationality of cubic threefolds, ordinary Gushel--Mukai threefolds, very general quartic fourfolds, and products of the threefolds with $\PP^1$.
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