Component Groups of Purely Toric Quotients

Component Groups of Quotients of J0(N)

Let f be a newform of weight 2 on Γ0(N), and let Af be the corresponding optimal abelian variety quotient of J0(N). We describe an algorithm to compute the order of the component group of Af at primes p that exactly divide N . We give a table of orders of component groups for all f of level N ≤ 127 and five examples in which the component group is very large, as predicted by the Birch and Swinn...

Quotients of Divisorial Toric

Toric quotients and flips

As my contribution to these proceedings, I will discuss the geometric invariant theory quotients of toric varieties. Specifically, I will show that quotients of the same problem with respect to different linearizations are typically related by a sequence of flips (or more precisely, log flips) in the sense of Mori, which in the quasi-smooth case can be characterized quite precisely. This seems ...

Quotients of Divisorial Toric Varieties

We consider subtorus actions on divisorial toric varieties. Here divisoriality means that the variety has many Cartier divisors like quasiprojective and smooth ones. We characterize when a subtorus action on such a toric variety admits a categorical quotient in the category of divisorial varieties. Our result generalizes previous statements for the quasiprojective case. A first step in the proo...

Fiber Fans and Toric Quotients

The GIT chamber decomposition arising from a subtorus action on a polarized quasiprojective toric variety is a polyhedral complex. Denote by Σ the fan that is the cone over the polyhedral complex. In this paper we show that the toric variety defined by the fan Σ is the normalization of the toric Chow quotient of a closely related affine toric variety by a complementary torus.