Jørgen Vold Rennemo

• Kool, Martijn; Oh, Jeongseok; Rennemo, Jørgen Vold & Thomas, Richard (2025). A Hopf index for isotropic sections of orthogonal bundles. arXiv. 2026(10). doi: 10.48550/ARXIV.2502.13050. Full text in Research Archive
• Kool, M. & Rennemo, Jørgen Vold (2025). Proof of a magnificent conjecture. arXiv. doi: 10.48550/ARXIV.2507.02852. Full text in Research Archive
• Lin, Xun; Rennemo, Jørgen Vold & Zhang, Shizhuo (2024). IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces. arXiv. doi: 10.48550/ARXIV.2408.08266. Full text in Research Archive
• Ottem, John Christian; Rennemo, Jørgen Vold & Kollár, János (2024). Fano varieties with torsion in the third cohomology group. Journal für die Reine und Angewandte Mathematik. ISSN 0075-4102. doi: 10.1515/crelle-2024-0020. Full text in Research Archive Show summary

  We construct first examples of Fano varieties with torsion in their third cohomology group. The examples are constructed as double covers of linear sections of rank loci of symmetric matrices, and can be seen as higher-dimensional analogues of the Artin–Mumford threefold. As an application, we answer a question of Voisin on the coniveau and strong coniveau filtrations of rationally connected varieties.

• Beentjes, Sjoerd Viktor; Calabrese, John & Rennemo, Jørgen Vold (2022). A proof of the Donaldson–Thomas crepant resolution conjecture. Inventiones Mathematicae. ISSN 0020-9910. doi: 10.1007/s00222-022-01109-w. Full text in Research Archive Show summary

  Abstract We prove the crepant resolution conjecture for Donaldson–Thomas invariants of hard Lefschetz 3-Calabi–Yau (CY3) orbifolds, formulated by Bryan–Cadman–Young, interpreting the statement as an equality of rational functions. In order to do so, we show that the generating series of stable pair invariants on any CY3 orbifold is the expansion of a rational function. As a corollary, we deduce a symmetry of this function induced by the derived dualising functor. Our methods also yield a proof of the orbifold DT/PT correspondence for multi-regular curve classes on hard Lefschetz CY3 orbifolds.

• Krug, Andreas & Rennemo, Jørgen Vold (2021). Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points. Mathematische Nachrichten. ISSN 0025-584X. 295(1), p. 158–174. doi: 10.1002/mana.201900351. Full text in Research Archive Show summary

  For X a smooth quasi-projective variety and 𝑋[𝑛] its associated Hilbert scheme of n points, we study two canonical Fourier–Mukai transforms 𝖣(𝑋)→𝖣(𝑋[𝑛]), the one along the structure sheaf and the one along the ideal sheaf of the universal family. For 𝖽𝗂𝗆𝑋≥2, we prove that both functors admit a left inverse. This means in particular that both functors are faithful and injective on isomorphism classes of objects. Using another method, we also show in the case of an elliptic curve that the Fourier–Mukai transform along the structure sheaf of the universal family is faithful and injective on isomorphism classes. Furthermore, we prove that the universal family of 𝑋[𝑛] is always flat over X, which implies that the Fourier–Mukai transform along its structure sheaf maps coherent sheaves to coherent sheaves.

• Rennemo, Jørgen Vold (2020). The homological projective dual of Sym² P(V ). Compositio Mathematica. ISSN 0010-437X. 156(3), p. 476–525. doi: 10.1112/S0010437X19007772. Full text in Research Archive Show summary

  We study the derived category of a complete intersection X of bilinear divisors in the orbifold Sym2P(V) . Our results are in the spirit of Kuznetsov’s theory of homological projective duality, and we describe a homological projective duality relation between Sym2P(V) and a category of modules over a sheaf of Clifford algebras on P(Sym2V∨) . The proof follows a recently developed strategy combining variation of geometric invariant theory (VGIT) stability and categories of global matrix factorisations. We begin by translating Db(X) into a derived category of factorisations on a Landau–Ginzburg (LG) model, and then apply VGIT to obtain a birational LG model. Finally, we interpret the derived factorisation category of the new LG model as a Clifford module category. In some cases we can compute this Clifford module category as the derived category of a variety. As a corollary we get a new proof of a result of Hosono and Takagi, which says that a certain pair of non-birational Calabi–Yau 3-folds have equivalent derived categories.

• Belmans, Pieter; Oberdieck, Georg & Rennemo, Jørgen Vold (2020). Automorphisms of Hilbert schemes of points on surfaces. Transactions of the American Mathematical Society. ISSN 0002-9947. 373(9), p. 6139–6156. doi: 10.1090/tran/8106. Full text in Research Archive Show summary

  We show that every automorphism of the Hilbert scheme of n points on a weak Fano or general type surface is natural, i.e., induced by an automorphism of the surface, unless the surface is a product of curves and n=2. In the exceptional case there exists a unique nonnatural automorphism. More generally, we prove that any isomorphism between Hilbert schemes of points on smooth projective surfaces, where one of the surfaces is weak Fano or of general type and not equal to the product of curves, is natural. We also show that every automorphism of the Hilbert scheme of 2 points on Pn is natural.

• Rennemo, Jørgen Vold; Segal, Ed & Bergh, Michel Van den (2019). A non-commutative Bertini theorem. Journal of Noncommutative Geometry. ISSN 1661-6952. 13(2), p. 609–616. doi: 10.4171/JNCG/334. Full text in Research Archive Show summary

  We prove a version of the classical ‘generic smoothness’ theorem with smooth varieties replaced by non-commutative resolutions of singular varieties. This in particular implies a non-commutative version of the Bertini theorem.

• Huybrechts, Daniel & Rennemo, Jørgen Vold (2019). Hochschild cohomology versus the Jacobian ring and the Torelli theorem for cubic fourfolds. Algebraic Geometry. ISSN 2313-1691. 6(1), p. 76–99. doi: 10.14231/AG-2019-005. Full text in Research Archive
• Rennemo, Jørgen Vold & Segal, Ed (2019). Hori-mological projective duality. Duke mathematical journal. ISSN 0012-7094. 168(11), p. 2127–2205. doi: 10.1215/00127094-2019-0014. Full text in Research Archive Show summary

  Kuznetsov has conjectured that Pfaffian varieties should admit noncommutative crepant resolutions which satisfy his Homological Projective Duality. We prove half the cases of this conjecture by interpreting and proving a duality of nonabelian gauged linear sigma models proposed by Hori.

• Ottem, John Christian & Rennemo, Jørgen Vold (2018). A counterexample to the birational Torelli problem for Calabi-Yau 3-folds. Journal of the London Mathematical Society. ISSN 0024-6107. 97(3), p. 427–440. doi: 10.1112/jlms.12111. Full text in Research Archive Show summary

  The Grassmannian Gr(2,5) is embedded in ℙ9 via the Pl\"ucker embedding. The intersection of two general PGL(10)-translates of Gr(2,5) is a Calabi-Yau 3-fold X, and the intersection of the projective duals of the two translates is another Calabi-Yau 3-fold Y, deformation equivalent to X. Applying results of Kuznetsov and Jiang-Leung-Xie shows that X and Y are derived equivalent, which by a result of Addington implies that their third cohomology groups are isomorphic as polarised Hodge structures. We show that X and Y provide counterexamples to a certain "birational" Torelli statement for Calabi-Yau 3-folds, namely, they are deformation equivalent, derived equivalent, and have isomorphic Hodge structures, but they are not birational.

• Rennemo, Jørgen Vold; Beentjes, Sjoerd & Calabrese, John (2018). A Proof of the Donaldson-Thomas Crepant Resolution Conjecture. arXiv.org. ISSN 2331-8422. Full text in Research Archive

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• Rennemo, Jørgen Vold (2023). K-theoretic sheaf counting invariants on C4. Full text in Research Archive
• Rennemo, Jørgen Vold (2023). Fano varieties with coniveau discrepancy. Full text in Research Archive
• Rennemo, Jørgen Vold (2021). The birational Torelli problem for Calabi–Yau 3-folds. Full text in Research Archive
• Rennemo, Jørgen Vold (2021). K-theoretic sheaf counting invariants of Quot schemes on C4. Full text in Research Archive
• Rennemo, Jørgen Vold (2021). K-theoretic sheaf counting invariants of Quot schemes on C4. Full text in Research Archive
• Rennemo, Jørgen Vold (2021). K-theoretic sheaf counting invariants of Quot schemes on C4. Full text in Research Archive
• Rennemo, Jørgen Vold (2021). Fixed-point loci in the Hilbert schemes of points in the plane. Full text in Research Archive

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