相关论文: A note on families of hyperelliptic curves
The main subject is the difference between the coarse moduli space and the stack of hyperelliptic curves. In particular, we compute their Picard groups, giving explicit description of the generators. We also study how many families of…
We compute the Picard group of the moduli stack of stable hyperelliptic curves of any genus, exhibiting explicit and geometrically meaningful generators and relations.
We present families of (hyper)elliptic curve which admit an efficient deterministic encoding function.
In this paper, we show that there exist families of curves (defined over an algebraically closed field $k$ of characteristic $p >2$) whose Jacobians have interesting $p$-torsion. For example, for every $0 \leq f \leq g$, we find the…
A new family of maximal curves over a finite field is presented and some of their properties are investigated.
We introduce the tautological rings of moduli stacks of twisted curves and establish some basic properties.
We prove the existence of tilting bundles on global quotient stacks that are produced by compatible finite group actions on flat families.
In this paper we give a presentation of the stack of trigonal curves as a quotient stack, and we compute its Picard group.
A new generalization of the classical separate algebraicity theorem is suggested and proved.
It is proved that the rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. As an illustration, we consider a family of elliptic curves with complex multiplication.
We construct families of hyperelliptic curves over Q of arbitrary genus g with (at least) g integral elements in K_2. We also verify the Beilinson conjectures about K_2 numerically for several curves with g=2, 3, 4 and 5. The paper is…
We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.
In this paper we study a family of curves obtained by fibre products of hyperelliptic curves. We then exploit this family to construct examples of curves of given genus g over a finite field Fq with many rational points. The results…
In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.
We find a new presentation of the stack of hyperelliptic curves of odd genus as a quotient stack and we use it to compute its integral Chow ring by means of equivariant intersection theory.
We describe a simple, but effective, method for deriving families of elliptic curves, with high rank, all of whose members have the same torsion subgroup structure.
The main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves. We compute their Picard groups, giving explicit description of the generators. We get an application to the…
In this thesis we prove Schur-positivity of certain graph families. In addition, we exlpor existence of cyclic descent extensions on several families of Schur-positive sets.
We give an elementary proof of the group law for elliptic curves using explicit formulas.
We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper.…