The Topology of Conjugate Varieties
نویسنده
چکیده
Serre [Se 64] and Abelson [Ab 74] have produced examples of conjugate algebraic varieties which are not homeomorphic. We show that if the field of definition of a polarized projective variety coincides with its field of moduli then all of its conjugates have the same topological type. This immediately extends the class of varietie s known to possess invariant topological type to all canonically embedded varieties. We also show that (normal) complete intersections in projective space and, more generally in homogeneous varieties, satisfy the condition.
منابع مشابه
OprF and OprL Conjugate as Vaccine Candidates against Pseudomonas aeruginosa; an in Silico Study
Introduction: Vaccine studies against Pseudomonas aeruginosa have often focused on outer membrane proteins (OPRs) due to their potent stimulation of the immune response. Using major outer membrane proteins of cell walls (mOMPs) of P. aeruginosa and other Gram-negative bacteria actively stimulate the immune system without any toxic side effects. Moreover, these antigens show immunological cross-...
متن کاملComplex Varieties and the Analytic Topology
Classical algebraic geometers studied algebraic varieties over the complex numbers. In this setting, they didn’t have to worry about the Zariski topology and its many pathologies, because they already had a better-behaved topology to work with: the analytic topology inherited from the usual topology on the complex numbers themselves. In this note, we introduce the analytic topology, and explore...
متن کاملNon-homeomorphic Conjugate Complex Varieties
We present a method to produce examples of non-homeomorphic conjugate complex varieties based on the genus theory of lattices. As an application, we give examples of arithmetic Zariski pairs.
متن کاملThe Geometry of Formal Varieties in Algebraic Topology I
Algebraic topology is full of computations with rings, and where we find rings we should seek geometry through methods of algebraic geometry. The geometry of formal varieties turn out to organize many interesting computations in topology, and certain formal varieties called commutative, one-dimensional formal groups give the best global picture of stable homotopy theory currently available. I w...
متن کاملThe Absolute Galois Group Acts Faithfully on the Connected Components of the Moduli Spaces of Surfaces of General Type
We show that the Galois group Gal(Q̄/Q) operates faithfully on the set of connected components of the moduli spaces of surfaces of general type, and also that for each element σ ∈ Gal(Q̄/Q) different from the identity and from complex conjugation, there is a surface of general type such that X and the Galois conjugate variety Xσ have nonisomorphic fundamental groups. The result was announced by t...
متن کامل