The equation xyz = x + y + z = 1 in integers of a cubic field.
The Equations for Modular Function Fields of Principal congruence subgroups of prime level.
The equations of space curves on a quadric.
The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves.
The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces
The Euler characteristic of the moduli space of curves.
The exponent of an abelian subvariety.
The fibre of the Prym map in genus four
In questa nota si dà una descrizione della fibra della mappa di Prym in genere 4. Se è la Jacobiana di una curva di genere 3, allora la fibra della mappa di Prym in si ottiene dalla varietà di Kummer mediante due scoppiamenti: che è lo scoppiamento di nell'origine e che è lo scoppiamento lungo una curva isomorfa a .
The Fibre of the Prym Map in Genus Three.
The field of definition of the Mordell-Weil group of an elliptic curve over a function field
The Fixed Points of the Symmetrie Hilbert Modular Group of a Real Quadratic Field with Arbitrary Discriminant.
The formal completion of the Néron model of J0(p).
For any prime number p > 3 we compute the formal completion of the Néron model of J0(p) in terms of the action of the Hecke algebra on the Z-module of all cusp forms (of weight 2 with respect to Γ0(p)) with integral Fourier development at infinity.
The fourth tautological group of and relations with the cohomology
We give a complete description of the fourth tautological group of the moduli space of pointed stable curves, , and prove that for it coincides with the cohomology group with rational coefficients. We further give a conjectural upper bound depending on the genus for the degree of new tautological relations.
The Frobenius action on rank vector bundles over curves in small genus and small characteristic
Let be a general proper and smooth curve of genus (resp. of genus ) defined over an algebraically closed field of characteristic . When , the action of Frobenius on rank semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order line bundle over . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp. the abelian...
The full automorphism group of the Kulkarni surface.
The full automorphism group of the Kulkarni surface is explicitly determined. It is employed to give three defining equations of the Kulkarni surface; each equation exhibits a symmetry of the surface as complex conjugation.
The fundamental group for the complement of Cayley's singularities.
The Fundamental Group of the Complement of an Algebraic Curve.
The Galois group of the tangency problem for plane curves.
The Galois structure of S-units
The Galois-module structure of the space of holomorphic differentials of a curve.
The Generic Torelli Theorem for the Prym Map.