## 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.

## Boundary of Siegel Modular Variety

The moduli space of curves has a compactification whose boundary can be understood as the product of moduli spaces of curves of lower genus. Therefore (perhaps naively) one might hope that there exists a compactification of $$A_g$$ whose boundary can be understood as in terms of the moduli of abelian varities of lower dimension. Is there any such compactification?

## ag.algebraic geometry – Holomorphic map from a Riemann surface to a smooth projective variety with Zariski-dense image

Let $$V$$ be a connected smooth projective complex variety. Does there exist a holomorphic map $$Sto V$$ with Zariski-dense image where $$S$$ is a Riemann surface without boundary (possibly of infinite genus)?

If $$V$$ is unirational we can compose the dominant rational map $$mathbb{A}^{mathrm{dim}: X}to V$$ with the map $$mathbb{A}^1to mathbb{A}^{mathrm{dim}:X}$$ given by $$zto big(e^z, e^{e^z}, dotsbig)$$ after possibly throwing out finitely points from $$mathbb{A}^1$$. If $$V$$ is an abelian variety the same idea works if we consider the surjective holomorphic (non-algebraic) map $$mathbb{A}^{mathrm{dim}:X}to V$$. It is not clear to me what happens for K3 surfaces.

## ag.algebraic geometry – Involution action on Brauer group of an abelian variety

Let $$k$$ be an algebraically closed field of characteristic $$p>2$$, let $$A/k$$ be an abelian variety. Let $$iotacolon Ato A, amapsto -a$$ be the natural involution. Let $$xinmathrm{Br}(A)(p)$$ be a Brauer class on $$A$$ of order $$p$$. Is it necessarily true that $$iota^*x=x$$?

## Is Projective variety isomorphic to some specific projective variety in P^N?

Show that any projective variety X is isomorphic to another
projective variety $$Y in P^{N}$$ for some N, whose ideal is generated by quadratic homogeneous polynomials.

## Any complex variety is diffeomorphic to a complex variety defined over \$mathbb{Q}\$

Given a smooth proper complex variety can you find a smooth proper complex variety defined over $$mathbb{Q}$$ that is diffeomorphic to it? For projective varieties you can approximate the defining equations (though even in this case I don’t think I can rigorously write down the details).

## Get balance for a variety of bitcoin core addresses

I am looking for a command to balance imported bitcoin addresses (not my wallet addresses) and I don't want to do this with blockchain explorer APIs. Is it possible to do this through the bitcoin core? if not, is there an alternative option like bitcore?

## ag.algebraic geometry – Count the image of a variety map using the plot formula

Suppose $$f: X a Y$$ is a finite map of varieties over a finite field $$mathbb F_q$$. Is there a constructible etale $$mathbb Q_ ell$$ sheaf $$mathscr F$$ in $$Y$$ which counts the number of rational points of the form $$f (x)$$ for $$x$$ itself rational (as an application of the tracking formula)?

Yes $$f$$ It is closed, we can only use the pushforward. On the other hand, even if $$X, Y$$ are both field spectra, let's say $$mathbb F_ {q ^ n}, mathbb F_q$$So I'm not sure what we want.

I think it could be easier to count $$deg (f)$$ multiplied by the number of points and that's fine too. For example, the number of squares in $$mathbb P ^ 1$$ is $$(q-1) / 2 + 2$$ but since the eigenvalues ​​are always $$q ^ { alpha}$$, it will be difficult to obtain a factor of $$q / 2$$ by cohomology calculations. But if we multiply by $$2$$, It's possible.

## dnd 5e – What books deal with gith (any variety) and the astral plane?

I'm looking for inspiration for a gith-based campaign on 5e and hope people can point me to any official book containing gith (either persuasion) or the astral plane they live on as focal points.

I'm only interested in narrative, so editing doesn't matter much, although I appreciate that some things have changed through editing.

While this might look like a 'do the job for me' question, I think it's my only option because buying every book from previous editions will quickly become expensive. Books can be of any kind (including novels) as long as they contain official information about the gith.

The only book I know of that contains a lot is Mordenkainens de 5e, which is what inspired the campaign. I am also aware of this question regarding the astral plane.

## dg. differential geometry: let \$ M ^ n \$ be a closed variety with \$ H_ {dR} ^ p (M) neq 0 \$. Generically, for any Riemannian metric \$ g \$, \$ K _ { max} / K _ { min} \$ does not depend on \$ p \$?

Leave $$M ^ n$$ be a closed variety in such a way that $$H_ {dR} ^ p (M) neq 0$$. Is it true that generically, for any Riemannian metric? $$g$$ in $$M$$, if one denotes by $$K$$ its sectional curvature, then
$$K _ { max} / K _ { min}$$ does not depend on $$p$$?

Note that this is a less restrictive question than asking what $$K _ { max} / K_ {min}$$ It does not depend on the dimension, I also do not know the conditions for this to happen.