Related papers: Non-Ulrich representation type

For any $n\geq 3$, we explicitly construct smooth projective toric $n$-folds of Picard number $\geq 5$, where any nontrivial nef line bundles are big.

Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces and van den Bergh's correspondence between representations of the generalized…

Given a partition $\lambda$ of n, consider the subspace $E_\lambda$ of $C^n$ where the first $\lambda_1$ coordinates are equal, the next $\lambda_2$ coordinates are equal, etc. In this paper, we study subspace arrangements $X_\lambda$…

Following a suggestion made by J.-P. Demailly, for each $k\ge 1$, we endow, by an induction process, the $k$-th (anti)tautological line bundle $\mathcal O_{X_k}(1)$ of an arbitrary complex directed manifold $(X,V)$ with a natural smooth…

Let $X$ be a connected CW complex. Let $\mathcal{V}$ be a symplectic vector bundle of rank $2mn$ over $X$, and let $\mathcal{A}$ be a topological Azumaya algebra of degree $2mn$ with a symplectic involution over a $X$. We give conditions…

Let $X$ be a geometrically irreducible smooth projective curve, of genus at least three, defined over the field of real numbers. Let $G$ be a connected reductive affine algebraic group, defined over $\mathbb R$, such that $G$ is nonabelian…

Let k be a field. In this paper, we find necessary and sufficient conditions for a noncommutative curve of genus zero over k to be a noncommutative P^1-bundle. This result can be considered a noncommutative, one-dimensional version of…

Let $X$ be a submanifold of dimension $d\geq 2$ of the complex projective space $\mathbb P^n$. We prove results of the following type. i) If $X$ is irregular and $n=2d$ then the normal bundle $N_{X|\mathbb P^n}$ is indecomposable. ii) If…

We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.

We prove some general results on syzygies of smooth projective varieties with numerically trivial canonical line bundle. This allows to confirm several cases of Mukai's syzygies conjecture for finite quotients of abelian varieties in any…

We consider all complex projective manifolds X that satisfy at least one of the following three conditions: 1. There exists a pair $(C ,\varphi)$, where $C$ is a compact connected Riemann surface and $\varphi : C\to X$ a holomorphic map,…

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the non quasi-split unramified unitary group in four variables defined over F_0. In this paper, we give a classification of the irreducible smooth…

The deformation of a variety $X$ to the normal cone of a subvariety $Y$ is a classical construction in algebraic geometry. In this paper we study the case when $(X,\omega)$ is a compact K\"ahler manifold and $Y$ is a submanifold. The…

We classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree. In the process, we prove the stability of the sheaves of relative differentials on rational scrolls.

In this paper, we investigate the existence of Ulrich bundles on a smooth complete intersection of two $4$-dimensional quadrics in $\mathbb P^5$ by two completely different methods. First, we find good ACM curves and use Serre…

We prove an elementary but somewhat unexpected result about projective embeddings of smooth varieties X whose cotangent bundles are numerically effective. Specifically, we show that the degree of X in any projective embedding must grow…

We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is…

Given a smooth del Pezzo surface $X_d \subseteq \mathbb{P}^{d}$ of degree $d,$ we show that a smooth irreducible curve $C$ on $X_d$ represents the first Chern class of an Ulrich bundle on $X_d$ if and only if its kernel bundle $M_C$ admits…

It is shown that if $X$ is an Inoue surface of type $S_M$ then the irreducible components of the Douady space of $X^n$ are compact, for all $n>0$. This gives an example of an essentially saturated compact complex manifold (in the sense of…

Let X be as smooth complex projective variety with Neron-Severi group isomorphic to Z, and D an irreducible divisor with normal crossing singularities. Assume r is equal to 2 or 3. We prove that if the fundamental group of X doesn't have…