Related papers: On divisorial (i) classes

We associate a combinatorial object to sequences of point blow-ups over perfect fields, the weighted directed graph, and another one to the composition of all blow-ups, which we call associated sequential morphisms, the $d-$ary intersection…

The naive blow-up algebras developed by Keeler-Rogalski-Stafford, after examples of Rogalski, are the first known class of connected graded algebras that are noetherian but not strongly noetherian. This failure of the strong noetherian…

Let $G$ be a connected algebraic group. We study $G$-equivariant extremal contractions whose centre is a codimension three $G$-simply connected orbit. In the spirit of an important result by Kawakita in 2001, we prove that those…

Let X be the blow-up of the projective plane in a finite set of very general points. We deduce from the work of Uehara that X has only standard autoequivalences, no nontrivial Fourier-Mukai partners, and admits no spherical objects. If X is…

In this paper we consider an effective divisor on the complex projective line and associate with it the module D consisting of all the derivations $\theta$ such that $\theta(I_i)\subset I_i^{m_i}$ for every $i$, where $I_i$ is the ideal of…

For every $n\geq 3$, we find a sufficient condition for the blow-up of a weighted projective space $\mathbb{P}(a,b,c,d_1,\cdots,d_{n-2})$ at the identity point not to be a Mori Dream Space. We exhibit several infinite sequences of weights…

We deal with a divisorial contraction in dimension 3 which contracts its exceptional divisor to a smooth point. We prove that any such contraction can be obtained by a suitable weighted blow-up.

Let $\Theta=(\theta_{jk})_{n\times n}$ be a real skew-symmetric $n\times n$ matrix for $n\geq 2$. Under some mild non-integrality conditions on $\Theta,$ we construct Rieffel-type projections as higher dimensional Bott classes in the…

In this paper, we prove that the divisor class group of a double cover of the complex projective space $\mathbb{P}^n$ is generated by divisorial sheaves whose direct images split into direct sums of two invertible sheaves on $\mathbb{P}^n$.…

We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution $v\in L^\infty (-1,0; L^2 ( B(x_0,r)))\cap L^\infty_{\rm loc} (-1,0; W^{1, \infty}…

We consider a natural generalisation of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and…

We prove that the partial derivative of the volume function of big classes along any real divisor in a compact Kaehler manifold is equal to the numerical restricted volume of that class to the divisor. A consequence of our main result is…

Motivated by the classical Theorems of Picard and Siegel and their generalizations, we define the notion of an {\it essentially large} effective divisor and derive some of its geometric and arithmetic consequences. We then prove that on a…

We give a condition for certain divisors on the blow up of P^3 at points in general position to be ample. The result extends a theorem of G. Xu on the blow up of the projective plane.

If $X$ is a smooth complex projective 3-fold with ample canonical divisor $K$, then the inequality $K^3\ge {2/3}(2p_g-7)$ holds, where $p_g$ denotes the geometric genus. This inequality is nearly sharp. We also give similar, but more…

We study interior $\varepsilon$-regularity and Type I blowup criteria for suitable weak solutions to the three-dimensional incompressible MHD equations. Our starting point is a direct iteration scheme for the classical…

We prove homology stability for elementary and special linear groups over rings with many units improving known stability ranges. Our result implies stability for unstable Quillen K-groups and proves a conjecture of Bass. For commutative…

Let $R$ be a commutative Noetherian ring with identity and $C$ a semidualizing module for $R$. Let $\mathscr{P}_C(R)$ and $\mathscr{I}_C (R)$ denote, respectively, the classes of $C$-projective and $C$-injective $R$-modules. We show that…

After a general discussion of group actions, orbifolds, and "weak orbifolds" this note will provide elementary introductions to two basic moduli spaces over the real or complex numbers: First the moduli space of effective divisors with…

In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na\"ive version of Andrews' anti-telescoping technique quite well. These new theorems also put to rest any notion…