Related papers: Ulrich bundles on some twisted flags
In this version referee's comments have been incorporated. Besides minor corrections, new material has been added on irrational markings. To appear in Ann. Inst. Fourier. We prove a condition for the existence of flat bundles on the…
We study the resolution of an Ulrich bundle of arbitrary rank on the Segre fourfold $\PP^2\times\PP^2$. We characterize the Ulrich bundles $\Vv$ of arbitrary rank on $\PP^2\times\PP^2$ with $h^1(\Vv\otimes\Omega\boxtimes\Omega)=0$ or with…
We define the odd symplectic grassmannians and flag manifolds, which are smooth projective varieties equipped with an action of the odd symplectic group and generalizing the usual symplectic grassmannians and flag manifolds. Contrary to the…
We prove a sharp Ohsawa-Takegoshi-Manivel type extension result for twisted holomorphic sections of singular hermitian line bundles over almost Stein manifolds. We establish as corollaries some extension results for pluri-twisted…
We characterize Kaehler manifolds with trivial logarithmic tangent bundle (with respect to a divisor D) as a class of certain compatifications of complex semi-tori.
We give an excluded minor characterisation of the class of ribbon graphs that admit partial duals of Euler genus at most one.
This note corrects a mistake in Theorem~4.1 of https://doi.org/10.1016/j.aim.2021.107598 (arXiv:1901.03395). The error noted here does not affect any other results of loc. cit. To correct the error, here I prove a more general result…
We determine the Picard number and the Ulrich complexity of general bidouble covers of the projective plane, providing the first systematic study of Ulrich bundles on non-cyclic abelian covers. For a bidouble plane branched along three…
We assume that $\mathcal{E}$ is a rank $r$ Ulrich bundle for $(P^n, \mathcal{O}(d))$. The main result of this paper is that $\mathcal{E}(i)\otimes \Omega^{j}(j)$ has natural cohomology for any integers $i \in \mathbb{Z}$ and $0 \leq j \leq…
We prove that suitable properties of the twists by Dirichlet characters of an L-function of degree 2 imply that its Euler product is of polynomial type.
We prove a conjecture of A. S. Buch concerning the structure constants of the Grothendieck ring of a flag variety with respect to its basis of Schubert structure sheaves. For this, we show that the coefficients in this basis of the…
Given a flag in each of the vertex-transitive tessellations of the Euclidean plane by regular polygons, we determine the flag stabilizer under the action of the automorphism group of a regular cover. In so doing we give a presentation of…
We investigate the behaviour of tilting sheaves under pushforward by a finite Galois morphism. We determine conditions under which such a pushforward of a tilting sheaf is a tilting sheaf. We then produce some examples of Severi Brauer flag…
For any V-twisted Higgs bundle on a compact Riemann surface X, where V is a holomorphic vector bundle of rank two on X, there are two associated Higgs bundles on X, twisted by line bundles, which are constructed using a Hecke transformation…
We classify all products of flag varieties with finitely many orbits under the diagonal action of the general linear group. We also classify the orbits in each case and construct explicit representatives. This generalizes the classical…
The existence of stable ACM vector bundles of high rank on algebraic varieties is a challenging problem. In this paper, we study stable Ulrich bundles (that is, stable ACM bundles whose corresponding module has the maximum number of…
We introduce a class of orders on $P^d$ called Geigle-Lenzing orders and show that they have tilting bundles. Moreover we show that their module categories are equivalent to the categories of coherent sheaves on Geigle-Lenzing spaces…
I provide a construction of intrinsic weakly Ulrich bundles of large rank on any smooth complete surface in ${\bf P}^3$ over fields of characteristic $p>0$ and also for some classes of surfaces of general type in ${\bf P}^n$. I also…
In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The…
In the present note, we will show that there are infinitely many composite twisted torus knots.