## Duke Mathematical Journal

Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

Shifted convolution sums for $\mathrm{GL}(3)\times\mathrm{GL}(2)$Volume 162, Number 13 (2013)
Three combinatorial formulas for type $A$ quiver polynomials and $K$ -polynomialsVolume 168, Number 4 (2019)
Stable bundles and integrable systemsVolume 54, Number 1 (1987)
On the rationality problem for quadric bundlesVolume 168, Number 2 (2019)
Isomonodromy deformations at an irregular singularity with coalescing eigenvaluesAdvance publication (2019)
• ISSN: 0012-7094 (print), 1547-7398 (electronic)
• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 1935--
• Access: By subscription only
• Euclid URL: https://projecteuclid.org/dmj

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MR Citation Database MCQ (2017): 2.45
JCR (2017) Impact Factor: 2.317
JCR (2017) Five-year Impact Factor: 2.539
JCR (2017) Ranking: 10/309 (Mathematics)
Article Influence (2017): 4.452
Eigenfactor: Duke Mathematical Journal
SJR/SCImago Journal Rank (2017): 6.155

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### Featured article

#### On the rationality problem for quadric bundles

Volume 168, Number 2 (2019)
##### Abstract

We classify all positive integers $n$ and $r$ such that (stably) nonrational complex $r$-fold quadric bundles over rational $n$-folds exist. We show in particular that, for any $n$ and $r$, a wide class of smooth $r$-fold quadric bundles over $\mathbb{P}^{n}_{\mathbb{C}}$ are not stably rational if $r\in[2^{n-1}-1,2^{n}-2]$. In our proofs we introduce a generalization of the specialization method of Voisin and of Colliot-Thélène and Pirutka which avoids universally $\mathrm{CH}_{0}$-trivial resolutions of singularities.

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