Search arXiv⌕ Search

arXiv · 0704.3339

Generators of Jacobians of Hyperelliptic Curves

Abstract

This paper provides a probabilistic algorithm to determine generators of the m-torsion subgroup of the Jacobian of a hyperelliptic curve of genus two.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Christian Robenhagen Ravnshoj. 2007-04-25. Generators of Jacobians of Hyperelliptic Curves. https://arxiv.org/abs/0704.3339

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Stability of the Cotangent Bundle on Surfaces with Ample Canonical Class

In this article, we study the Bridgeland stability of the cotangent bundle on K3 surfaces and surfaces with ample canonical class. On a surface $X$ with ample canonical class $K$, we find values $t_0>0$ such that the cotangent bundle is semistable with respect to the Bridgeland stability $σ_{tK}$ for all $t > t_0$. We also study special cases such as the fake projective planes and the fake quadrics.

math.AG↗

From wall structures to closed mirror symmetry. The case of $K_{\mathbb{P}^2}$: Renormalized periods over the positive real locus, closed Gromov-Witten invariants from wall functions, and tropical enumeration

We recover closed Gromov-Witten invariants and renormalized mirror periods for $K_{\mathbb{P}^2}$ by the same operation on a wall function. This gives a direct passage from the Gross-Siebert construction of intrinsic mirror pairs to classical enumerative mirror symmetry. The link is a polynomiality theorem for punctured invariants. Assuming the expected identification with the normalized slab function, we also obtain a finite tree sum for closed Gromov-Witten invariants in terms of types of plane tropical curves. The mechanism is expected to extend to more general Calabi-Yau mirror pairs.

math.AG↗

The topology of Kähler manifolds and 1-forms without zeros

We study how the topology and geometry of a compact Kähler manifold relate to the zeros of its one-forms. We determine all implications among several closely related conditions. In particular, we construct a smooth projective variety for which the Aomoto complex is exact for every nonzero holomorphic one-form and every semisimple local system, although every closed real one-form, and hence every holomorphic one-form, has a zero.

math.AG↗