183 research outputs found
Geometry over composition algebras : projective geometry
The purpose of this article is to introduce projective geometry over
composition algebras : the equivalent of projective spaces and Grassmannians
over them are defined. It will follow from this definition that the projective
spaces are in correspondance with Jordan algebras and that the points of a
projective space correspond to rank one matrices in the Jordan algebra. A
second part thus studies properties of rank one matrices. Finally, subvarieties
of projective spaces are discussed.Comment: 24 page
On Mukai flops for Scorza varieties
I give three descriptions of the Mukai flop of type , one in terms
of Jordan algebras, one in terms of projective geometry over the octonions, and
one in terms of O-blow-ups. Each description shows that it is very similar to
certain flops of type . The Mukai flop of type is also
described.Comment: 35
Maximal representations of uniform complex hyperbolic lattices in exceptional Hermitian Lie groups
We complete the classification of maximal representations of uniform complex
hyperbolic lattices in Hermitian Lie groups by dealing with the exceptional
groups and . We prove that if is a maximal
representation of a uniform complex hyperbolic lattice , , in an exceptional Hermitian group , then and , and we describe completely the representation . The case of
classical Hermitian target groups was treated by Vincent Koziarz and the second
named author (arxiv:1506.07274). However we do not focus immediately on the
exceptional cases and instead we provide a more unified perspective, as
independent as possible of the classification of the simple Hermitian Lie
groups. This relies on the study of the cominuscule representation of the
complexification of the target group. As a by-product of our methods, when the
target Hermitian group has tube type, we obtain an inequality on the Toledo
invariant of the representation which is stronger
than the Milnor-Wood inequality (thereby excluding maximal representations in
such groups).Comment: Comments are welcome
On stratified Mukai flops
We construct a resolution of stratified Mukai flops of type A, D, E_{6, I} by
successively blowing up smooth subvarieties. In the case of E_{6, I}, we
construct a natural functor which induces an isomorphism between the Chow
groups.Comment: use diagrams.st
Idée et réalité : sur la lecture pragmatique de Hegel, la certitude sensible et le mythe du donné
La visĂ©e de ce texte est dâintroduire le lecteur francophone Ă lâinterprĂ©tation pragmatique de Hegel essentiellement prĂ©sente dans le monde anglo-saxon. LâintĂ©rĂȘt grandissant au sein de la francophonie pour ce genre de lecture nous porte Ă questionner le sens mĂȘme du qualificatif « pragmatique » qui la caractĂ©rise. Cette prĂ©cision faite, nous nous attarderons Ă la figure de la certitude sensible dans la PhĂ©nomĂ©nologie de lâesprit en y soulignant les thĂšmes pragmatiques, notamment dans le cas de ce que Wilfrid Sellars aurait appelĂ© une critique du mythe du donnĂ©
Les interprétations féministes du concept d'état de nature chez Hobbes : une clé de lecture
Pour comprendre lâorigine des diffĂ©rentes interprĂ©tations fĂ©ministes portant sur la famille et le patriarcat chez Hobbes, il faut avoir pour clĂ© de lecture la double comprĂ©hension possible de lâĂ©tat de nature. Une premiĂšre lecture fait de lâĂ©tat de nature un outil dĂ©monstratif dans un systĂšme logique, alors quâune seconde lecture en fait une hypothĂšse historique sur la genĂšse de nos institutions. Comprendre la distinction entre une lecture purement logique et une lecture plus historisante de lâĂ©tat de nature peut permettre une meilleure comprĂ©hension des diffĂ©rentes interprĂ©tations fĂ©ministes. En effet, nous tenterons de dĂ©montrer que derriĂšre ces positions polarisĂ©es se cache une lecture diffĂ©rente de lâĂ©tat de nature chez Hobbes
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