Related papers: Projective normality of Abelian threefolds

In this paper, we prove that the normal bundle of a general Brill-Noether space curve of degree $d$ and genus $g \geq 2$ is stable if and only if $(d,g) \not\in \{ (5,2), (6,4) \}$. When $g\leq1$ and the characteristic of the ground field…

We give a $K$-theoretic criterion for a quasi-projective variety to be smooth. If $\mathbb{L}$ is a line bundle corresponding to an ample invertible sheaf on $X$, it suffices that $K_q(X) = K_q(\mathbb{L})$ for all $q\le\dim(X)+1$.

We give conditions under which natural lines bundles associated with completions of period mappings are semi-ample and ample.

The moduli space of abelian surfaces with polarisation of type (1,t) and a bilevel structure is of general type if t is odd and at least 17.

The main problem addressed in the paper is the Torelli problem for n-dimensional varieties of general type, more specifically for varieties with ample canonical bundle. It asks under which geometrical condition for a variety the period map…

This paper is mainly concerned with applying the theory of M-regularity developed in the previous math.AG/0110003 to the study of linear series given by multiples of ample line bundles on abelian varieties. We define a new invariant of a…

We investigate finite 3-nets embedded in a projective plane over a (finite or infinite) field of any characteristic p. Such an embedding is regular when each of the three classes of the 3-net comprises concurrent lines, and irregular…

Let $\mathbb{X}$ be a Geigle-Lenzing projective plane of type $(2,2,2,p)$ and $\mathsf{coh} \mathbb{X}$ the category of coherent sheaves on $\mathbb{X}$. This paper is devoted to study ACM tilting bundles over $\mathbb{X}$, that is, tilting…

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,…

Studying coverings over algebraic varieties is an effective method in algebraic geometry. By combining the technique of triple cover from Miranda and Tan, we proved that if the degree of the branch divisor of a normal triple cover over…

This work consists of two parts. In the first part we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic surfaces.…

Let $C$ be a general canonical curve of genus $g$ defined over an algebraically closed field of arbitrary characteristic. We prove that if $g \notin \{4,6\}$, then the normal bundle of $C$ is semistable. In particular, if $g \equiv 1$ or…

Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists…

Let $X$ be a projective variety over a field. In this paper, we will construct a moduli space of very ample line bundles on $X$. In doing so, we develop a generalization of Fitting ideals to complexes of sheaves on $X$. We give other…

We describe birational models and decide the rationality/unirationality of moduli spaces AA_{d} (and AA^{lev}_{d}) of (1,d)-polarized abelian surfaces (with canonical level structure, respectively) for small values of d. The projective…

Using multigraded Castelnuovo-Mumford regularity, we study the equations defining a projective embedding of a variety X. Given globally generated line bundles B_1, ..., B_k on X and integers m_1, ..., m_k, consider the line bundle L :=…

We prove that ribbons, i.e. double structures associated with a line bundle $\SE$ over its reduced support, a smooth irreducible projective curve of arbitrary genus, are smoothable if their arithmetic genus is greater than or equal to $3 $…

We carry out the classification of abelian Lie symmetry algebras of two-dimensional second-order nondegenerate quasilinear evolution equations. It is shown that such an equation is linearizable if it admits an abelian Lie symmetry algebra…

Let $C$ be the rational normal curve of degree $e$ in $\mathbb{P}^n$, and let $X\subset \mathbb{P}^n$ be a degree $d\ge 2$ hypersurface containing $C$. In previous work, I. Coskun and E. Riedl showed that the normal bundle $N_{C/X}$ is…

We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated…