相关论文: Prym enumerative geometry and a Hurwitz divisor in…

In this paper we classify curves of genus two over a perfect field k of characteristic two. We find rational models of curves with a given arithmetic structure for the ramification divisor and we give necessary and sufficient conditions for…

The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to…

For an affine double plane defined by an equation of the form z^2 = f, we study the divisor class group and the Brauer group. Two cases are considered. In the first case, f is a product of n linear forms in k[x,y] and X is birational to a…

We study Shimura curves of PEL type in $\mathsf{A}_g$ generically contained in the Prym locus. We study both the unramified Prym locus, obtained using \'etale double covers, and the ramified Prym locus, corresponding to double covers…

We use a rigidity argument to prove the existence of two related degree twenty-eight covers of the projective plane with Galois group SU3(3).2 = G2(2). Constructing corresponding two-parameter polynomials directly from the defining…

In this paper we compute the pullback of divisor classes under the Prym map (extended to the boundary), and apply this result to get a lower bound on the slope of effective divisors on the perfect cone compactification of the moduli space…

Let $\varphi:\Sigma_1\longrightarrow \mathbb{P}^2$ be a blow up at a point on $\mathbb{P}^2$. Let $C$ be the proper transform of a smooth plane curve of degree $d\geq 4$ by $\varphi$, and let $P$ be a point on $C$. Let…

This paper shows Hurwitz integrality of the coefficients of expansion at the origin of the sigma function \(\sigma(u)\) associated to a certain plane curve which should be called a plane telescopic curve. For the prime \(2\), the expansion…

Let $\phi:\,X\rightarrow Y$ be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of $\phi$, up to isogeny, as the Jacobian of a quotient curve $C$ in the Galois…

Single Hurwitz numbers enumerate branched covers of the Riemann sphere with specified genus, prescribed ramification over infinity, and simple branching elsewhere. They exhibit a remarkably rich structure. In particular, they arise as…

The Maroni stratification on the Hurwitz space of degree $d$ covers of genus $g$ has a stratum that is a divisor only if $d-1$ divides $g$. Here we construct a stratification on the Hurwitz space that is analogous to the Maroni…

We compute the degree of Hurwitz-Hodge classes $\lambda_1^e$ on one dimensional moduli spaces of cyclic admissible covers of the projective line. We also compute the degree of the the first Chern class of the Hodge bundle $\lambda_1$ for…

We compute the class of arithmetic genus two Teichmueller curves in the Picard group of pseudo-Hilbert modular surfaces, distinguished according to their torsion order and spin invariant. As an application, we compute the number of genus…

We prove orientation results for evaluation maps of moduli spaces of rational stable maps to del Pezzo surfaces over a field, both in characteristic $0$ and in positive characteristic. These results and the theory of degree developed in a…

We develop techniques for using compactifications of Hurwitz spaces to study families of rational maps $\mathbb{P}^1\to\mathbb{P}^1$ defined by critical orbit relations. We apply these techniques in two settings: We show that the parameter…

This survey grew out of notes accompanying a cycle of lectures at the workshop Modern Trends in Gromov-Witten Theory, in Hannover. The lectures are devoted to interactions between Hurwitz theory and Gromov-Witten theory, with a particular…

This article is an extended version of preprint math.AG/9902104. We find an explicit formula for the number of topologically different ramified coverings of a sphere by a genus g surface with only one complicated branching point in terms of…

We compute the rank of the first homology group and we study the higher Betti numbers of the real points of the Deligne-Mumford-Knudsen compactification of stable n-pointed curves of genus 0,which coincides with the Chow quotient…

We recursively compute the Gromov-Witten invariants of the Hilbert scheme of two points in the plane. By studying the space of stable maps and computing virtual contributions, we use these invariants to enumerate hyperelliptic plane curves…

We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based not on bad reduction of curves, but on a very explicit…