Related papers: Stacks of trigonal curves
We prove that the Brauer group of TMF is isomorphic to the Brauer group of the derived moduli stack of elliptic curves. Then, we compute the local Brauer group, i.e., the subgroup of the Brauer group of elements trivialized by some \'etale…
We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack [point/GL(1)], and use it to construct some gauge-theoretic analogues of the Gromov-Witten invariants. We also indicate the…
In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components…
Let $X$ be a smooth projective curve over the complex numbers. We compute the Brauer group of the moduli stack of Bruhat-Tits group scheme $\mathcal{G}$-torsors on $X$. When $g(X) \geq 3$ we compute the Brauer group of the regularly stable…
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…
Let S be a site. We introduce the notion of extensions of strictly commutative Picard S-stacks. We define the pull-back, the push-down, and the sum of such extensions and we compute their homological interpretation: if P and Q are two…
We determined the Picard group of the moduli of rank two stable sheaves on an arbitrary algebraic surface up to finite index
In this series of three papers we start to investigate the rational Chow ring of the stack consisting of nodal curves of genus 0, in particular we determine completely the rational Chow ring of the substack consisting of curves with at most…
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coeficients in $\K$. We compute the semigroup Poincar\'e…
This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the $n$-torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these…
We compute the cohomological invariants of $\mathcal{H}_g$, the moduli stack of smooth hyperelliptic curves, for every odd $g$.
We outline a proof that the stack of symplectic toric G-manifolds over a fixed orbit space W is a torsor for the stack of symplectic toric G-principal bundles over W.
We introduce a theory of cohomological invariants with mod $p^r$ coefficients for algebraic stacks in characteristic $p$. Using these new tools we complete the computation of the Brauer group and cohomological invariants of the stack of…
From any monoid scheme $X$ (also known as an $\mathbb{F}_1$-scheme) one can pass to a semiring scheme (a generalization of a tropical scheme) $X_S$ by scalar extension to an idempotent semifield $S$. We prove that for a given irreducible…
We start with $n$-torsions in the Jacobian of an $m$-gonal curve and produce $n$-torsions in the class group of certain number field $K$.
Starting from a collection of line bundles on a projective toric orbifold X, we introduce a stacky analogue of the classical linear series. Our first main result extends work of King by building moduli stacks of refined representations of…
The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed…
The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.
We address the problem of computing in the group of $\ell^k$-torsion rational points of the jacobian variety of algebraic curves over finite fields, with a view toward computing modular representations.
We describe an algorithm for computing the Picard-Fuchs equation for a family of twists of a fixed elliptic surface. We then apply this algorithm to obtain the equation for several examples, which are coming from families of Kummer surfaces…