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I have an explicit genus one curve $E$ with two points $p_1$ and $p_2$ on it and am looking for an explicit degree seven cover $X\to E$ with ramification precisely over $p_i$, with a single preimage p …

Has anyone come across anything along the following lines? Let $X_1(p)$ be the compactification of the quotient of upper half plane by $\Gamma_1(p)$ for some unspecified large prime. Let $X_1(p) \to …

Bernd Sturmfels and others have studied varieties defined by binomial ideals. This is what you are looking for.

Let $X$ be a curve embedded into a projective space $\mathbb P$ such that it is cut out (scheme-theoretically or ideal-theoretically) by quadrics. What is known about the Koszul dual of the homogene …

Let $X$ be a smooth scheme of finite type over $\mathbb Q$ or $\mathbb Z$. It is natural to consider $D(X)$, the derived category of coherent sheaves on $X$. Beyond the definition, have there been any …

You can think of this ring as the semigroup ring of the semigroup $S$ generated by $$(1,0,0,1),(-1,0,0,1),(0,1,0,1),(0,-1,0,1),(0,0,1,1),(0,0,-1,1).$$ The above semigroup elements correspond to $f_1,f …

Let's see what happens in dim 2. You have $conv((0,0),(ra_1+sb_1,0),(0,ra_2+sb_2))$. The number of points in the closed triandle $(0,0),(A,0),(0,B)$ is $(A+1)(B+1)/2$ plus half the number of points on …

If you are willing to work with smooth stacks, rather than smooth toric varieties (or alternatively consider toric varieties with quotient singularities) then it is definitely possible. Combinatoria …

There seems to be some terminology drift here. I would say that "order" would be called degree in modern terminology, for example. Here is the way I see it, and please someone correct me if I am wron …

Is there a reference for generators of fundamental groups of (some) fake projective planes in terms of matrices in $SU(2,1)$?

I assume you mean dim 3 ODPs? The $A_1$ singularity typically refers to surface ODPs. I don't think such variety can be constructed. On the fan side, the minimum generators of the rays form somethin …

I assume that you mean $x_1=x_2=0$ in your description of the divisors. I believe that you only really get two different resolutions, but yes, they are both projective varieties. Hodge numbers of bira …

Suppose I have a curve $C$ defined over $\mathbb Q$ and a line bundle $\mathcal L$ on it, also defined over $\mathbb Q$. I am interested in trying to find a (non-effective) divisor $D=\sum_i a_ip_i$ o …

This is pretty much straightforward curiosity. Is there anything known about Newton polygons of classical modular polynomials (polynomial relations between $j(\tau)$ and $j(n\tau)$)? I understand that …

In his work on mirror symmetry (http://arxiv.org/pdf/alg-geom/9502005v2.pdf) Igor Dolgachev has considered families of K3 surfaces of Picard rank at least 19 with the base given by $X_0(n)^+$, the quo …