The Fermi surface for the discretized Maxwell equations
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 for dynamical systems on
The field of definition of the Mordell-Weil group of an elliptic curve over a function field
The field of moduli of abelian surfaces with complex multiplication.
The field of moduli of quaternionic multiplication on abelian varieties.
The First Cohomology Group of a Line Bundle on G/B.
The Fixed Point Subvarieties of Unipotent Transformations on Generalized Flag Varieties and the Green Functions. Combinatorial and Cohomological Treatments Centering GLn.
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 Formal Hodge Filtration.
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 at infinity of affine surfaces.
The fundamental group for the complement of Cayley's singularities.
The fundamental group of a Galois cover of .
The fundamental group of a locally finite graph with ends-a hyperfinite approach
The end compactification |Γ| of a locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally, we give...
The Fundamental Group of the Complement of a Union of Complex Hyperplanes.