9 citations · 19 across the 13 of their papers we have counts for
16 papers
Hirzebruch signature theorem on Hochschild homology, with applications to derived invariance of Hodge numbers
Roland Abuaf
We prove a refinement of Hirzebruch's signature formula on the individual Hochschild diagonals of a smooth projective complex variety. Natural Hermitian forms, obtained by symmetri…
Holomorphic symplectic manifolds from semistable Higgs bundles
Roland Abuaf, Riccardo Carini
Let be the moduli space of semistable rank two and degree zero Higgs bundles on a smooth complex hyperelliptic curve of genus three. We prove that the q…
On the twisted octonionic eigenvalue problem and some sextics hypersurfaces related to the Cartan cubic
Roland Abuaf
We revisit the octonionic eigenvalue problem from a geometric perspective. In particular, we study a tautological sheaf defined on a sextic related to this problem, the Ogievetskiî…
Derived invariance of the numbers
Roland Abuaf
Let and be derived equivalent smooth projective varieties over the field of complex numbers. We prove that the numbers and are equal for a…
Gradings of Lie algebras, magical spin geometries and matrix factorizations
Roland Abuaf, Laurent Manivel
We describe a remarkable rank fourtenn matrix factorization of the octic Spin(14)-invariant polynomial on either of its half-spin representations. We observe that this representati…
Hodge numbers and Hodge structures for Calabi-Yau categories of dimension three
Roland Abuaf
Let be a smooth proper C-linear triangulated category Calabi-Yau of dimension 3 endowed with a (non-trivial) rank function. Using the homological unit of $\mathcal{A}…
On quartic double fivefolds and the matrix factorizations of exceptional quaternionic representations
Roland Abuaf
We study quartic double fivefolds from the perspective of Fano manifolds of Calabi-Yau type and that of exceptional quaternionic representations. We first prove that the generic qu…
Scheme-theoretic Whitney conditions and applications to tangency of projective varieties
Roland Abuaf
We investigate a scheme-theoretic variant of Whitney condition a. If X is a projec-tive variety over the field of complex numbers and Y X a subvariety, then X satisfies g…
Compact hyper-Kähler categories
Roland Abuaf, Grégoire Menet
We define and study the notion of hyper-Kähler category. On the theoretical side, we focus on construction techniques and deformation theory of such categories. We also study in de…
Homological units
Roland Abuaf
We define and study the invariance properties of homological units. Some applications are given to the derived invariance of Hodge numbers. In particular, we prove that if X and Y…
Categorical crepant resolutions for quotient singularities
Roland Abuaf
We discuss some "folklore" results on categorical crepant resolutions for varieties with quotient singularities.
Orthogonal bundles and skew-Hamiltonian matrices
Roland Abuaf, Ada Boralevi
Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space of stable rank orthogonal vector bundles on $\m…
Categorical crepant resolutions of singularities and the Tits-Freudenthal magic square
Roland Abuaf
We prove that the tangent developables of the varieties appearing in the third row of the Tits-Freudenthal magic square admit categorical crepant resolutions of singularities.
Wonderful resolutions and categorical crepant resolutions of singularities
Roland Abuaf
Let be an algebraic variety with Gorenstein singularities. We define the notion of a wonderful resolution of singularities of by analogy with the theory of wonderful compac…
Theorems on tangencies in projective and convex geometry
Roland Abuaf
We discuss various phenomena of tangency in projective and convex geometry.
Singularities of the Projective Dual Variety
Roland Abuaf
We study the singularities of the projective dual variety.