Related papers: Rational self-maps of moduli spaces

This informal note provides some elementary examples to motivate the local structural results of [1] on the moduli space of genus one stable maps to projective space. The hope is that these examples will be helpful for graduate students to…

The moduli spaces of trigonal curves of odd genus $g>4$ are proven to be rational.

By associating to a curve C of genus g=2k and a pencil of degree d=k+1 the so-called trace curve (resp. the reduced trace curve) we define a rational map from the Hurwitz space of admissible covers of genus g=2k and degree d=k+1 to a moduli…

In this, largely expository, note, we show how the simplicial structure of the moduli spaces of stable rational curves with marked points allows to produce explicit equations for these spaces. The key argument is an elementary combinatorial…

The global geometry of the moduli spaces of higher spin curves and their birational classification is largely unknown for g >= 2 and r > 2. Using quite related geometric constructions, we almost complete the picture of the known results in…

We prove that the moduli space of curves with level structures has an enormous amount of rational cohomology in its cohomological dimension. As an application, we prove that the coherent cohomological dimension of the moduli space of curves…

This paper is to give some concrete examples of the general fibers of the evaluation map of some Kontsevich mapping spaces parametrize low degree rational curves on low degree complete intersection varieties. We prove these examples are…

We determine all of lines in the moduli space $M$ of stable bundles for arbitrary rank and degree. A further application of minimal rational curves is also given in last section.

Let $C$ be an algebraic curve of genus $g$ and $L$ a line bundle over $C$. Let $\mathcal{MS}_C(n,L)$ and $\mathcal{MO}_C(n,L)$ be the moduli spaces of $L$-valued symplectic and orthogonal bundles respectively, over $C$ of rank $n$. We…

A lot is known about the moduli space of parabolic bundles over curves of genus $g\geq 2$, but the lower genus cases are notably different. The goal of this article is to study the geometry of the moduli space of semistable parabolic…

The paper aims to give an account, both historical and geometric, on the diverse geography of rational parametrizations of moduli spaces related to curves. It is a contribution to the book Handbook of Moduli, editors G. Farkas and I.…

The moduli spaces of trigonal curves are proven to be rational when the genus is divisible by 4.

We prove that the moduli space of plane curves of degree d is rational for all sufficiently large d.

We prove that the moduli spaces of rational curves of degree at most $3$ in linear sections of the Grassmannian $Gr(2,5)$ are all rational varieties. We also study their compactifications and birational geometry.

We collect various known results (about plane curves and the moduli space of stable maps) to derive new recursive formulas enumerating low genus plane curves of any degree with various behaviors. Recursive formulas are given for the…

We investigate low degree rational cohomology groups of smooth compactifications of moduli spaces of curves with level structures. In particular, we determine $H^k(\sgbar, \Q)$ for $g \ge 2$ and $k \le 3$, where $\sgbar$ denotes the moduli…

To every covering of curves, we associate several varieties having the same field of moduli and same fields of definition. We deduce examples of curves having Q (the field of rationals) as field of moduli, that admit models over any…

Motivated by several recent results on the geometry of the moduli spaces $\bar{\Cal M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, here we determine their birational structure for small values of $g$ and $n$ by exploiting…

We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.

We compute the rational cohomology of the moduli space of non-singular complex projective curves of genus 3 with two marked points.