Real varieties associated to complex varieties

Real abelian varieties with complex multiplication

Prym Varieties Associated to Graphs

We present a Prym construction which associates abelian varieties to vertex-transitive strongly regular graphs. As an application we construct Prym-Tyurin varieties of arbitrary exponent ≥ 3, generalizing a result by Lange, Recillas and Rochas.

Real and Complex Regularity are Equivalent for Hyperbolic Characteristic Varieties

In the trivial case of P being a constant, both varieties are empty. Taking η = 0 shows that P (θ) 6= 0. If P is of degree m ≥ 1, then for each η ∈ R, the equation P (η + sθ) = 0 has m real roots counting multiplicity so the line η + sθ cuts the varieties V in at least 1 and no more than m points. It follows that VR (resp. VC) is a real algebraic variety (resp. algebraic variety) of real (resp....

Orientability of Real Toric Varieties

We characterize the orientability of an abstract real toric variety as well as the orientability of a toric subvariety of a sphere. We also determine the number of components of the smooth locus of a toric variety. These results are proven for an extension of the Davis-Januskiewicz notion of a small cover to singular spaces. We characterize the orientability of toric varieties associated to pos...

Enumerative Geometry for Real Varieties

Of the geometric figures in a given family satisfying real conditions, some figures are real while the rest occur in complex conjugate pairs, and the distribution of the two types depends subtly upon the configuration of the conditions. Despite this difficulty, applications ([7],[28],[32]) may demand real solutions. Fulton [11] asked how many solutions of an enumerative problem can be real, and...