## ag.algebraic geometry – Distinguishing ample divisors by minimally intersecting curves on a projective simplicial toric variety

My question has an easily formulated generalization, which I will state first. Let $$sigma subseteq mathbf{R}^n$$ be a strongly convex polyhedral cone. For each minimally generating lattice point $$m in sigma^o cap mathbf{Z}^n$$ of the interior cone $$sigma^o subseteq sigma$$, let $$S(m) subseteq sigma^{vee} cap mathbf{Z}^n$$ denote the set of lattice points $$u$$ with $$langle u,m rangle = 1$$. My question is:

Does $$S(m) = S(m’)$$ imply that $$m = m’$$?

As a special case, assume that $$sigma$$ is the nef cone of a simplicial projective toric variety $$X_{Sigma}$$. Then my question seems to amount to the following:

If $$D_1$$ and $$D_2$$ are two ample divisors minimally generating in the ample cone, then does $$D_1 cdot C = 1 Leftrightarrow D_2 cdot C = 1$$ for all effective curves $$C$$ imply that $$D_1 = D_2$$?

This is the case I am most interested in.

## ag.algebraic geometry – Degree inequality of a polynomial map distinguishing hyperplanes

Let $$H_1, ldots, H_m$$ be $$m$$ linearly independent hyperplanes in $$k^n$$, for some arbitrary field $$k$$. Let $$X = H_1 cup H_2 cup cdots cup H_m$$. Is it true that if $$F=(f_1, ldots, f_r)$$ is a polynomial map from $$k^n$$ to $$k^r$$, such that $$F(X) cap F(k^n – X) = emptyset$$, then $$sum deg(f_i) ge m$$?

This holds under the stronger condition that for all $$a in X$$, $$F(a)$$ has at least one coordinate equal to zero, and for all $$a notin X$$, $$F(a)$$ has all coordinates nonzero: $$prod f_i$$ then cuts out $$X$$, but since any polynomial cutting out $$X$$ has degree at least $$m$$, the conclusion follows.

I am particularly interested in the case when $$deg(f_i) = 2$$.

(I apologize if this problem is too easy for here. I posted it on MSE first, but it didn’t get attention.)

## compilers: problems distinguishing between syntax-driven translation and syntax-driven definition

I am currently reading the dragon book, chapter 2 confuses me a lot
Accordingly, the definition of the two terms are:

syntax-driven translation

Syntax-driven translation is done by attaching rules or snippets of programs or productions in a grammar

I understand that in a production within {} we have some rules / program code running (those rules / program are also known as semantic action)

syntax driven definition

A syntax driven definition is associated
1.With each grammatical symbol, a set of attributes, and
2. With each production, a set of semantic rules for calculating the values ​​of the attribute associated with the symbols that appear in the production

I understand this definition is that with each production we associate an action at the end of the queue to calculate the value of an attribute (this action is also known as semantic rules)

I have some doubts regarding the two definitions.
1. Is my understanding of these two definitions correct?

1. Why do syntax-driven translation and syntax-driven definition do the same task using two different ways?

2. Is a syntax-driven translation scheme the same as syntax-driven translation?

3. What is the difference between the syntax-driven translation scheme and just the translation scheme?

## Lens: What are the distinguishing features of several Sony mirrorless camera models?

I am not a professional photographer and it is basically my hobby.

I would like to buy a camera without a mirror and I have thought about getting `Sony a6000`.

Most of the time I take pictures of the landscape and the night sky / moon and I liked that the camera I was buying also had good photos.

So far I have used `Canon sx60hs` the camera and the images were satisfactory, however, I would like to have something better (this camera also has a crazy zoom).

My doubts are mainly about the differences between:

``````Sony a6000 ~ 650\$
Sony a6400 ~ 1190\$
Sony a6500 ~ 1220\$
``````

I read that there are no big differences between them (yes, the a6000 is from 2014) and I wonder if the difference is worth almost double the price.

Any other recommendation for a camera of the same level will be appreciated and also the recommendation for the Sony a6000 lens for landscape / night sky can also help.

Thank you!