Related papers: Ulrich complexity and categorical representability…
We prove the existence of Ulrich bundles on any Brauer--Severi variety. In some cases, the minimal possible rank of the obtained Ulrich bundles equals the period of the Brauer--Severi variety. Moreover, we find a formula for the rank of an…
In this paper we prove that a finite product of Brauer--Severi varieties is categorical representable in dimension zero if and only if it admits a $k$-rational point if and only if it is rational over $k$. The same is true for certain…
Our concern in this paper is the dimension and inclusion relations of Schubert varieties in twisted partial affine flag varieties. In the end we apply our results to some local models of certain Schubert varieties.
This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…
In this paper, we give a relation between the Hilbert multiplicity and the irreducible multiplicity. As an application, we characterize Ulrich modules in term of the irreducible multiplicity.
In this note we prove that certain twisted flag varieties carry Ulrich bundles.
We introduce the notion of primitive Ulrich bundle in a smooth projective variety. We motivate this notion and give a cohomological characterization in the case of the degree $6$ flag threefold and rational normal scrolls. Finally we…
We generalize the results by Eisenbud and Schreyer about Ulrich bundles over Veronese varieties to Segre-Veronese varieties. We discuss the range where we have natural cohomology and we construct multigraded resolutions and monads for…
We give examples of surfaces which are Ulrich-wild, i.e. that support families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$.
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…
Given a projective variety $X$ and a very ample line bundle $\mathcal{L}$ on $X$, we classify for which $X$ and $\mathcal{L}$ the twisted syzygies and twisted dual syzygies bundles are Ulrich with respect to the polarizations…
In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…
We provide a natural interpretation of the secondary Euler characteristic and introduce higher Euler characteristics. For a compact oriented manifold of odd dimension, the secondary Euler characteristic recovers the Kervaire…
In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra $C_f$ of a ternary cubic form $f$ and certain vector bundles (called Ulrich bundles) on a cubic surface $X$.…
A classification of double flag varieties of complexity 0 and 1 is obtained. An application of this problem to decomposing tensor products of irreducible representations of semisimple Lie groups is considered.
On any smooth $n$-dimensional variety we give a pretty precise picture of rank $r$ Ulrich vector bundles with numerical dimension at most $\frac{n}{2}+r-1$. Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo…
An Ulrich sheaf on an embedded projective variety is a normalized arithmetically Cohen-Macaulay sheaf with the maximum possible number of independent sections. Ulrich sheaves are important in the theory of Chow forms, Boij-Soderberg theory,…
This paper investigates Ulrich bundles on decomposable threefold scrolls X over the Hirzebruch surface $\mathbb F_a$, for any integer $a \geq 0$, focusing on the study of their structure and classification. We prove existence of such Ulrich…
Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…
Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure…