The rationality of the moduli space of two-pointed ineffective spin hyperelliptic curves

The rationality of the moduli space of one-pointed ineffective spin hyperelliptic curves via an almost del Pezzo threefold

Using the geometry of an almost del Pezzo threefold, we show that the moduli space of genus $g$ one-pointed ineffective spin hyperelliptic curves is rational for every $g\geq 2$.

无效 spin 亏格 4 thetanull 轨迹的有理性

The rationality of ineffective spin genus-4 thetanull loci

本文证明了由亏格4且thetanull消失的曲线C与无效thetacharacteristic θ构成的对[C,θ]所给出的除子是有理簇，并得出Prym模空间中的类似除子也是有理的。

About the equivalence of divisor classes on hyperelliptic curves and a quotient of linear forms by an algebraic group action

For a hyperelliptic curve of genus $g$, a divisor in general position of degree $g+1$ is given by polynomial equations. There is an action from an algebraic group on the representations of divisors by polynomials which fixes divisor classes. This structure reduces the question of rationality of divisor classes to rationality of polynomials which is more easy to control.

Hyperelliptic and trigonal Fano threefolds

We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein singularities which are not intersections of quadrics. We also study the rationality questions for most of these varieties.

Division by 2 on hyperelliptic curves and jacobians

Let $K$ be an algebraically closed field of characteristic different from 2, $g$ a positive integer, $f(x)$ a degree $(2g+1)$ polynomial with coefficients in $K$ and without multiple roots, $C: y^2=f(x)$ the corresponding genus $g$ hyperelliptic curve over $K$ and $J$ the jacobian of $C$. We identify $C$ with the image of its canonical embedding into $J$ (the infinite point of $C$ goes to the zero point of $J$). For each point $P=(a,b)\in C(K)$ there are $2^{2g}$ points $\frac{1}{2}P \in J(K)$. We describe explicitly the Mumford represesentations of all $\frac{1}{2}P$. The rationality question…

射影空间循环覆盖的tautological族

Tautological families of cyclic covers of projective spaces

本文研究射影空间循环覆盖的tautological族存在性，给出存在条件并确定相关模空间的有理性，受超椭圆曲线模空间工作启发。