Related papers: Remarks on diagonal dimension for algebraic stacks
For a toric Deligne-Mumford (DM) stack, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism on a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the…
We study extension properties for morphisms of stacks of bundles for group algebraic spaces. Applications are a short proof of the classification of bundles on the projective line for smooth geometrically reductive groups and the existence…
In this paper we will show that the pull-back of any regular differential form defined on the smooth locus of a good quotient of dimension three and four to any resolution yields a regular differential form.
In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball…
In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally,…
In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of…
In this paper, we define a new dimension for objects in a Grothendieck category $\mathcal{A}$. We show that it serves as a lower bound for Gabriel-Krull dimension and under certain conditions, the two dimensions coincide. We carry out our…
In this article we construct a categorical resolution of singularities of an excellent reduced curve $X$, introducing a certain sheaf of orders on $X$. This categorical resolution is shown to be a recollement of the derived category of…
To each associative unitary finite-dimensional algebra over a normal base, we associative a canonical multiplicative function called its determinant. We give various properties of this construction, as well as applications to the topology…
We study the moduli space of logarithmic connections of rank 2 on the Riemann sphere minus n points with fixed spectral data. There are two natural Lagrangian maps: one towards apparent singularities of the associated fuchsian scalar…
In this article we obtain lower and upper bounds for global dimensions of a class of artinian algebras in terms of global dimensions of a finite subset of their artinian subalgebras. Finding these bounds for the global dimension of an…
We compute several types of dimension for the bounded derived categories of coherent sheaves of orbifold curves. This completes the calculation of these dimensions for derived categories of noncommutative curves in the sense of Reiten-van…
Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie…
We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers various known statements in the literature. As applications…
Given a smooth projective toric variety $X$ of Picard rank 2, we resolve the diagonal sheaf on $X \times X$ by a linear complex of length $\dim{X}$ consisting of finite direct sums of line bundles. As applications, we prove a new case of a…
For a Noetherian scheme $X$ of finite Krull dimension, Neeman recently established two characterizations of the regularity of $X$ using strong generators and bounded $t$-structures on $\operatorname{Perf}(X)$. In this note, we obtain…
We give upper bounds on the essential dimension of (quasi-)simple algebraic groups over an algebraically closed field that hold in all characteristics. The results depend on showing that certain representations are generically free. In…
In this paper, we determine upper bound for the non-abelian tensor product of finite dimensional Lie superalgebra. More precisely, if $L$ is a non-abelian nilpotent Lie superalgebra of dimension $(k \mid l)$ and its derived subalgebra has…
We extend the notion of representability dimension to partial actions and introduce a notion of dual representability dimension for global actions by finite abelian groups. We show that the Rokhlin dimension of a partial action by a finite…
Let $H$ be the quantum double of a Nichols algebra of diagonal type. We compute the $R$-matrix of 3-uples of modules for general finite-dimensional highest weight modules over $H$. We calculate also a multiplicative formula for the…