Related papers: Curves over finite fields and moduli spaces
In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of…
It is a well known result that the number of points over a finite field on the Legendre family of elliptic curves can be written in terms of a hypergeometric function modulo $p$. In this paper, we extend this result, due to Igusa, to a…
This is the authors doctoral thesis written at the Humboldt-University Berlin. It contains material from the three separate papers: "On the Kodaira dimension of the moduli space of nodal curves", "On quotients of…
This work is a PhD thesis. First we provide some general context on wonderful varieties and moduli spaces of rational curves. Working over complex numbers we prove that the moduli space of rational curves with no marked points on the…
We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…
We show that under mild boundary conditions the moduli space of non-compact curves on a complex surface is (locally) an analytic subset of a ball in a Banach manifold, defined by {\it finitely} many holomorphic function.
Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.
We study the moduli space ${V}_4\mathcal{M}_{g}$ of Klein four covers of genus $g$ curves and its natural compactification. This requires the construction of a related space which has a choice of basis for the Klein four group. This space…
We shall study moduli spaces of stable 1-dimensional sheaves on an elliptic ruled surface.
In this paper, we establish the compactification of the moduli space in symplectization and and studied the hidden symmetries of its boundary.
This is a survey paper: we discuss certain recent results, with some improvements. It will appear in the S. Cruz proceedings.
As an introduction to the concept of "moduli space" we consider the moduli space of similarity classes of acute and right triangles in the plane. This has a map to the moduli space of elliptic curves which is onto and generically…
We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…
One of the big questions in the area of curves over finite fields concerns the distribution of the numbers of points: Which numbers occur as the number of points on a curve of genus $g$? The same question can be asked of various subclasses…
In this expository note, we offer an overview of the relationship between Hodge-theoretic and geometric compactifications of moduli spaces of algebraic varieties.