Related papers: Divisor class groups of graded hypersurfaces

We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The…

We give an explicit description of the divisor class groups of rational trinomial varieties. As an application, we relate the iteration of Cox rings of any rational variety with torus action of complexity one to that of a Du Val surface.

In this work we use arithmetic, geometric, and combinatorial techniques to compute the cohomology of Weil divisors of a special class of normal surfaces, the so-called rational ruled toric surfaces. These computations are used to study the…

We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…

We shall describe the divisor class group and the graded canonical module of the multi-section ring for a normal projective variety X and Weil divisors D_1,..., D_s on X under a mild condition. In the proof, we use the theory of Krull…

For a hyperelliptic curve of genus $g$, a divisor in general position of degree $g+1$ is given by polynomial equations. There is an action from an algebraic group on the representations of divisors by polynomials which fixes divisor…

We determine the rational divisor class group of the moduli spaces of smooth pointed hyperelliptic curves and of their Deligne-Mumford compactification, over the field of complex numbers.

Consider the subset of a Weyl group with a fixed descent set. For Weyl groups of classical types, we determine the number of two-sided cells this subset intersect. Moreover, we apply this result to prove that certain rational Whittaker…

We present an algorithm for computing the 2-group of the positive divisor classes of a number field F in case F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel WK2(F) in K2(F) for such number…

The main goal of this paper is to show that the notions of Weil and Cartier $\mathbb{Q}$-divisors coincide for $V$-manifolds and give a procedure to express a rational Weil divisor as a rational Cartier divisor. The theory is illustrated on…

The aim of this paper is to study Weil divisors on a singular rational normal scroll X. In particular the author describes explicitly the group of divisorial sheaves associated to Weil divisors on X, via the direct image of the Picard group…

We show that it is possible to utilize the Hirzebruch-Milnor classes of projective hypersurfaces in the classical sense to detect higher du Bois or rational singularities only in some special cases. We also give several remarks clarifying…

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 $\mathbb{P}^n$.…

Theorem: If W is a smooth complex projective variety with h^1 (O-script_W) = 0, then a sufficiently ample smooth divisor X on W cannot be a hyperplane section of a Calabi-Yau variety, unless W is itself a Calabi-Yau. Corollary: A smooth…

We compute the fake degrees of representations of classical Weyl groups in terms of domino tableaux.

We address the question of effectivity for calculation of local Weil functions from the viewpoint of presentations of Cartier divisors. This builds on the approach of Bombieri and Gubler as well as the perspective of our earlier works.…

We present an algorithm that determines the Galois group of linear difference equations with rational function coefficients.

The Welschinger invariants of real rational algebraic surfaces count real rational curves which represent a given divisor class and pass through a generic conjugation-invariant configuration of points. No invariants counting real curves of…

We apply the differential Galois theory for difference equations developed by Hardouin and Singer to compute the differential Galois group for a second-order linear $q$-difference equation with rational function coefficients. This Galois…

We calculate the classes of the universal hyperelliptic Weierstrass divisor $\bar{{\mathcal H}}_{g,w}$ and the universal $g^1_2$ divisor $\bar{{\mathcal H}}_{g,g^1_2}$. Our results are expressed in terms of a basis for $Cl(\bar{{\mathcal…