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Equivalence classes of Latin squares and nets in ℂ P 2

Corey Dunn, Matthew Miller, Max Wakefield, Sebastian Zwicknagl (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The fundamental combinatorial structure of a net in ℂ P 2 is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in ℂ P 2 . Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in ℂ P 2 are empty to show some non-existence results for 4-nets in ℂ P 2 .

Equivalence of families of singular schemes on threefolds and on ruled fourfolds.

Flaminio Flamini (2004)

Collectanea Mathematica

The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for families of...

Equivariant degenerations of spherical modules for groups of type A

Stavros Argyrios Papadakis, Bart Van Steirteghem (2012)

Annales de l’institut Fourier

V. Alexeev and M. Brion introduced, for a given a complex reductive group, a moduli scheme of affine spherical varieties with prescribed weight monoid. We provide new examples of this moduli scheme by proving that it is an affine space when the given group is of type A and the prescribed weight monoid is that of a spherical module.

Equivariant Euler characteristics and sheaf resolvents

Ph. Cassou-Noguès, M.J. Taylor (2012)

Annales de l’institut Fourier

For certain tame abelian covers of arithmetic surfaces we obtain formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler characteristics of both the canonical sheaf and also its square root. These formulas allow us to carry out explicit calculations; in particular, we are able to exhibit examples where these two Euler characteristics and that of the structure sheaf are all different and non-trivial. Our results are obtained by using resolvent techniques...

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