Related papers: Explicit stable models of elliptic surfaces with s…
We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil…
We give a classification of the log canonical models of elliptic surface pairs consisting of an elliptic fibration, a section, and a weighted sum of marked fibers. In particular, we show how the log canonical models depend on the choice of…
This is the third paper in a series of work on weighted stable elliptic surfaces - elliptic fibrations with section and marked fibers weighted between zero and one. Motivated by Hassett's weighted pointed stable curves, we use the log…
We present explicit equations of semi-stable elliptic surfaces (i.e., having only type $I_n$ singular fibers) which are associated to the torsion-free genus zero congruence subgroups of the modular group as classified by A. Sebbar.
This paper deals with a study of the rational elliptic surfaces whose $J$-invariant functions are of degree one. Almost all of these elliptic surfaces have four singular fibers, while the remaining surfaces have only three singular fibers.…
We recast elliptic surfaces over the projective line in terms of the non-commutative tori and one-parameter families of the periodic continued fractions. The correspondence is used to study the Picard numbers, the ranks and the minimal…
We study the elliptic modular surface attached to the commutator subgroup of the modular group. This has an elliptic curve as base and only one singular fibre. We employ an algebraic approach and then consider some arithmetic questions.
We shall study moduli spaces of stable 1-dimensional sheaves on an elliptic ruled surface.
Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…
In this paper we consider coherent systems $(E,V)$ on an elliptic curve which are stable with respect to some value of a parameter $\alpha$. We show that the corresponding moduli spaces, if non-empty, are smooth and irreducible of the…
We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in positive characteristic, as well as about log smooth…
In this paper, we construct stable distributions on the set of elliptic elements of an odd orthogonal groups (over a p-adic field with p large). Theses distributions are of zero level. They are parametrised by Langlands like parameters. In…
In this article, we construct an infinite sequence of irreducible components of Koll\'{a}r--Shepherd-Barron (KSB-) moduli spaces of surfaces of arbitrarily large volumes, and describe the boundary of each component completely. Moreover, we…
Consider genus $g$ curves that admit degree $d$ covers to elliptic curves only branched at one point with a fixed ramification type. The locus of such covers forms a one parameter family $Y$ that naturally maps into the moduli space of…
We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction…
We give the parameters of any evaluation code on a smooth quadric surface. For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes on elliptic quadrics are obtained by detecting a BCH…
We show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.
We study the stable pair theory on toric surfaces and determine the virtual tangent space over the fixed point loci. Further, we present a program to compute the virtual Euler characteristic, illustrated by the case of the projective plane.…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
It is well-known that in any codimension a simply connected Euclidean minimal surface has an associated one-parameter family of minimal isometric deformations. In this paper, we show that this is just a special case of the associated family…