24 citations · 79 across the 15 of their papers we have counts for
16 papers
Factorisability in K-theory
Jørgen Vold Rennemo
We revisit and give a detailed proof of a lemma of Okounkov showing that, for a scheme X with a torus action, the Euler characteristic generating function associated with a "factor…
Proof of a magnificent conjecture
M. Kool, J. V. Rennemo
Motivated by super-Yang-Mills theory on a Calabi-Yau 4-fold, Nekrasov and Piazzalunga have assigned weights to -tuples of solid partitions and conjectured a formula for their we…
A Hopf index for isotropic sections of orthogonal bundles
Martijn Kool, Jeongseok Oh, Jørgen Vold Rennemo +1
The Hopf index equates the multiplicity of a zero of a section of a vector bundle with a winding number. We give eight analogues for isotropic sections of bundles with quadratic fo…
IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces
Xun Lin, Jørgen Vold Rennemo, Shizhuo Zhang
We study the categorical Torelli theorem for smooth (weighted) hypersurfaces in (weighted) projective spaces via the Hochschild--Serre algebra of its Kuznetsov component. In the fi…
Fano varieties with torsion in the third cohomology group
John Christian Ottem, Jørgen Vold Rennemo
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 symmetr…
Automorphisms of Hilbert schemes of points on surfaces
Pieter Belmans, Georg Oberdieck, Jørgen Vold Rennemo
We show that every automorphism of the Hilbert scheme of points on a weak Fano or general type surface is natural, i.e. induced by an automorphism of the surface, unless the su…
A proof of the Donaldson-Thomas crepant resolution conjecture
Sjoerd Viktor Beentjes, John Calabrese, Jørgen Vold Rennemo
We prove the crepant resolution conjecture for Donaldson-Thomas invariants of hard Lefschetz CY3 orbifolds, formulated by Bryan-Cadman-Young, interpreting the statement as an equal…
Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points
Andreas Krug, Jørgen Vold Rennemo
For a smooth quasi-projective variety and its associated Hilbert scheme of points, we study two canonical Fourier--Mukai transforms , the one…
A counterexample to the birational Torelli problem for Calabi-Yau threefolds
John Christian Ottem, Jørgen Vold Rennemo
The Grassmannian Gr(2,5) is embedded in via the Plücker embedding. The intersection of two general PGL(10)-translates of Gr(2,5) is a Calabi-Yau 3-fold X, and the inter…
The fundamental theorem of homological projective duality via variation of GIT stability
Jørgen Vold Rennemo
We reprove Kuznetsov's "fundamental theorem of homological projective duality" using LG models and variation of GIT stability. This extends the validity of the theorem from smooth…
A non-commutative Bertini theorem
Jørgen Vold Rennemo, Ed Segal, Michel Van den Bergh
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 n…
Hochschild cohomology versus the Jacobian ring, and the Torelli theorem for cubic fourfolds
Daniel Huybrechts, Jørgen Rennemo
The Jacobian ring J(X) of a smooth hypersurface determines its isomorphism type. This has been used by Donagi and others to prove the generic global Torelli theorem for hypersurfac…
Hori-mological projective duality
Jørgen Vold Rennemo, Ed Segal
Kuznetsov has conjectured that Pfaffian varieties should admit non-commutative crepant resolutions which satisfy his Homological Projective Duality. We prove half the cases of this…
The homological projective dual of Sym^2 P(V)
Jørgen Vold Rennemo
We study the derived category of a complete intersection X of bilinear divisors in the orbifold Sym^2 P(V). Our results are in the spirit of Kuznetsov's theory of homological proje…
Homology of Hilbert schemes of points on a locally planar curve
Jørgen Vold Rennemo
Let C be a proper, integral, locally planar curve, and consider its Hilbert schemes of points C^[n]. We define 4 creation/annihilation operators acting on the rational homology gro…
Universal Polynomials for Tautological Integrals on Hilbert Schemes
Jørgen Vold Rennemo
We show that tautological integrals on Hilbert schemes of points can be written in terms of universal polynomials in Chern numbers. The results hold in all dimensions, though they…