The arithmetic-geometric mean and isogenies for curves of higher genus
The Artin algebras associated with differential operators on singular affine curves.
The associated map of the nonabelian Gauss-Manin connection
The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.
The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces.
The automorphism group of
The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of is the permutation group on elements as soon as .
The automorphism group of the modular curve
The automorphism group of the moduli space of semi stable vector bundles.
The automorphism groups of Zariski open affine subsets of the affine plane
We study some properties of the affine plane. First we describe the set of fixed points of a polynomial automorphism of ℂ². Next we classify completely so-called identity sets for polynomial automorphisms of ℂ². Finally, we show that a sufficiently general Zariski open affine subset of the affine plane has a finite group of automorphisms.
The average rank of elliptic curves I. With Appendix "The Explicit formula for elliptic curves over function fields" by Oisín McGuinness.
The Brauer group of desingularization of moduli spaces of vector bundles over a curve
Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M C (r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧r E = L. We show that the Brauer group of any desingularization of M C(r; L) is trivial.
The Brauer–Manin obstruction for curves having split Jacobians
Let be a non-constant morphism from a curve to an abelian variety , all defined over a number field . Suppose that is a counterexample to the Hasse principle. We give sufficient conditions for the failure of the Hasse principle on to be accounted for by the Brauer–Manin obstruction. These sufficiency conditions are slightly stronger than assuming that and are finite.
The Briançon-Skoda number of analytic irreducible planar curves
The Briançon-Skoda number of a ring is defined as the smallest integer k, such that for any ideal and , the integral closure of is contained in . We compute the Briançon-Skoda number of the local ring of any analytic irreducible planar curve in terms of its Puiseux characteristics. It turns out that this number is closely related to the Milnor number.
The canonical constellations of k-Weierstrass points.
The canonical height and integral points on elliptic curves.
The Cassels-Tate pairing on polarized Abelian varieties.
The characteristic polynomial of a monodromy transformation attached to a family of curves.
The Chow ring of the stack of cyclic covers of the projective line
In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.
The class group of a one-dimensional affinoid space
A curve over a non-archimedean valued field is with respect to its analytic structure a finite union of affinoid spaces. The main result states that the class group of a one dimensional, connected, regular affinoid space is trivial if and only if is a subspace of . As a consequence, has locally a trivial class group if and only if the stable reduction of has only rational components.
The Clifford dimension of a projective curve
The compactified Jacobian