Related papers: Rationality of some tetragonal loci

F. Campana had asked whether a certain threefold is rational. In arXiv:1310.3569v1 [mathAG], this variety was shown to be birational to a specific conic bundle and then to be unirational. We prove that this conic bundle is rational.

We show that the moduli space of degree $e$ maps from smooth genus $g \ge 1$ curves to an arbitrary low degree smooth hypersurface is singular when $e$ is large compared to $g$. We also give a lower bound for the dimension of the singular…

For any non-simply laced Lie group $G$ and elliptic curve $\Sigma$, we show that the moduli space of flat $G$ bundles over $\Sigma$ can be identified with the moduli space of rational surfaces with $G$-configurations which contain $\Sigma$…

We study how the degrees of irrationality of moduli spaces of polarized K3 surfaces grow with respect to the genus $g$. We prove that the growth is bounded by a polynomial function of degree $14+\varepsilon$ for any $\varepsilon>0$ and, for…

We study moduli spaces $M_X(r,c_1,c_2)$ parametrizing slope semistable vector bundles of rank $r$ and fixed Chern classes $c_1, c_2$ on a ruled surface whose base is a rational nodal curve. We show that under certain conditions, these…

We study the gonality and canonical model of a rational unicuspidal curve C. We are mainly interested in the case where C is non-Gorenstein. We classify such curves via different notions of gonality, and by its canonical model C', up to…

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…

It is a classical result that there are $12$ (irreducible) rational cubic curves through $8$ generic points in $\mathbb{P}_{\mathbb{C}}^2$, but little is known about the non-generic cases. The space of $8$-point configurations is…

We consider the moduli space of parabolic connections with rational generic weights over a compact Riemann surface of genus $g \geq 3$. We determine the Chow group of the moduli space of parabolic connections such that the underlying…

We compute the rational cohomology of the moduli space $\mathcal{M}_{4,1}$ of non-singular genus $4$ curves with $1$ marked point, using Gorinov-Vassiliev's method.

The open subvariety $\overline{M}_g^{\leq k}$ of $\overline{M}_g$ parametrizes stable curves of genus $g$ having at most $k$ rational components. By the work of Looijenga, one expects that the cohomological excess of $\overline{M}_g^{\leq…

Let $r \geq 2, d$ be two integers which are coprime to each other. Let $C$ be a smooth projective curve of genus $g \geq 2$ and $M(r,L)$ be the moduli space of rank $r$ stable vector bundles on $C$ whose determinants are isomorphic to a…

Principally polarized abelian surfaces with prescribed real multiplication (RM) are parametrized by certain Hilbert modular surfaces. Thus rational genus 2 curves correspond to rational points on the Hilbert modular surfaces via their…

We prove that a complete family of linearly non-degenerate rational curves of degree $e > 2$ in $\mathbb{P}^n$ has at most $n-1$ moduli. For $e = 2$ we prove that such a family has at most $n$ moduli. It is unknown whether or not this is…

Let $C$ be a general canonical curve of genus $g$ defined over an algebraically closed field of arbitrary characteristic. We prove that if $g \notin \{4,6\}$, then the normal bundle of $C$ is semistable. In particular, if $g \equiv 1$ or…

In [3], it is proved that the quotient of an abelian variety $A$ by a finite order automorphism $g$ is uniruled if and only if some power of $g$ satisfies a numerical condition $0<\age(g^k)<1$. In this paper, we show that $\age(g^k)=1$ is…

For any standard quadric surface bundle over $\mathbb P^2$, we show that the locus of rational fibres is dense in the moduli space.

K3 surfaces with non-symplectic symmetry of order 3 are classified by open sets of twenty-four complex ball quotients associated to Eisenstein lattices. We show that twenty-two of those moduli spaces are rational.

We build a database of genus 2 curves defined over $\mathbb Q$ which contains all curves with minimal absolute height $h \leq 5$, all curves with moduli height $\mathfrak h \leq 20$, and all curves with extra automorphisms in standard form…