Related papers: Adjoint $(1,1)$-classes on threefolds

We show the abundance theorem for arithmetic klt threefold pairs whose closed point have residue characteristic greater than five. As a consequence, we give a sufficient condition for the asymptotic invariance of plurigenera for certain…

We utilise a quotient of the universal enveloping algebra of the Poincar\'e algebra in three spacetime dimensions, on which we formulate a covariant constancy condition. The equations so obtained contain the Fierz-Pauli equations for…

We determine the possible Hilbert functions of graded rank one torsion free modules over three dimensional Artin-Schelter regular algebras. It turns out that, as in the commutative case, they are related to Castelnuovo functions. From this…

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…

In this article we present a refinement of the base point free theorem for threefolds in positive characteristic. If $L$ is a nef Cartier divisor of numerical dimension at least one on a projective Kawamata log terminal threefold…

Let $G$ be a smooth connected linear algebraic group over a field $k$, and let $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d \geq 1$, then does $X$ have a closed \'etale point of degree dividing $d$? We give an…

We exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. We also prove the $3$ - divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic…

We describe the possible Mordell-Weil groups for degree 1 elliptic threefold with rational base and constant $j$-invariant. Moreover, we classify all such elliptic threefolds if the $j$-invariant is nonzero. We can use this classification…

We shall develop a theory of multi-pointed non-commutative deformations of a simple collection in an abelian category, and construct relative exceptional objects and relative spherical objects in some cases. This is inspired by a work by…

The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kahler manifold. As a consequence we obtain several results on…

Working over a field of characteristic zero, we give structure theorems for all grade three licci ideals and their minimal free resolutions. In particular, we completely classify such ideals up to deformation. The descriptions of their…

In this paper we introduce a class of mathematical objects called \emph{extensors} and develop some aspects of their theory with considerable detail. We give special names to several particular but important cases of extensors. The…

Let $(X,D)$ be log canonical pair such $\dim X = 3$ and the divisor $-(K_X + D)$ is nef and big. For a special class of such $(X,D)$'s we prove that the linear system $|-n(K_{X}+D)|$ is free for $n \gg 0$.

Tridendriform algebras are a type of associative algebras, introduced independently by F. Chapoton and by J.-L. Loday and the third author, in order to describe operads related to the Stasheff polytopes. The vector space $\st$ spanned by…

We prove a type of the Lefschetz hyperplane section theorem on Q-Fano 3-folds with Picard number one and $1/2(1,1,1)$-singularities by using some degeneration method. As a byproduct, we obtain a new example of a Calabi-Yau 3-fold $X$ with…

We prove that there exist infinitely many (-1,1)-Carmichael numbers, that is, square-free, composite integers n such that p+1 divides n-1 for each prime p dividing n.

For a tuple $(\theta_1,..,\theta_M)$ of complex number, buliding on the approximation techniques in earlier papers of this series, this paper engages in deducing lower estimates on the transcendence degree of the field generated by…

For a prime p and natural number n with p greater than or equal to n, we establish the existence of a non-functorial one-to-one correspondence between isomorphism classes of groups of order p^n whose derived subgroup has exponent dividing…

This article characterizes the associativity of two-place functions $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(F(f(x),f(y)))$ where $F:[0,1]^2\rightarrow[0,1]$ is a triangular norm (even a triangular subnorm), $f:…

Let $P(x):=a_d x^d+\cdots+a_0\in\mathbb{Q}[x]$, $a_d>0$, be a polynomial of degree $d\geq 2$. Let $(x_n)$ be a sequence of integers satisfying \begin{equation*} x_{n+1}=P(x_n)\mbox{for all}\quad n=0,1,2\ldots,\quad\mbox{and} \quad…