## Properties of Javelin Quiver?

One of my players wishes to carry javelins. It seems logical that these could be carried in a quiver (appropriately sized of course) that would reside on the wearer’s back and would serve a similar function as a quiver does for arrows.

We cannot find any reference material for such a thing (how much it would cost, how many javelins it would hold). Is there a place where such a thing is specified?

## Greater Invisibility vs Swift Quiver

The scene: A level 10 College of Swords Bard (includes extra attack). Crossbow Expert. Sharpshooter. 20 Dexterity. Hand crossbow + 1.

Intelligence is his dump stat so he needs to ask a friend what to pick for his magical secret.

One is definitely Find Greater Steed, because he is going to ride on a griffon while raining down death with his hand crossbow. The other may or may not be Swift Quiver.

Greater Invisibility will give me 2 attacks with my action, 1 attack as a bonus action, +10 to hit with advantage.

Swift Quiver will give me 2 attacks with my action, 2 attacks with my bonus action, +10 to hit.

Ignoring opportunity costs, spell slots costs, defence and anything else other than crossbow damage per round, at what point is it better to use Swift Quiver vs Greater Invisibility?

## Would drawing darts from a “dart quiver” use up your free item interaction?

A follow on question from Is drawing an arrow from a quiver an item interaction?, using throwing darts. This time I have, let’s say, a level 1 Dex-based Fighter who has two shortswords and darts. He duel wields, but there’s an enemy that’s just out of melee range, even after closing the gap with his movement, so he wants to throw a dart at them.

Can he sheath one sword, then throw the dart as his Attack Action without needing another Action to draw the darts (let’s assume they’re not buried in a backpack but instead strapped to the outside of his leather armour or something, in other words they’re easily accessible like arrows in a quiver). Again, I’m ignoring the “drop the sword” option for this hypothetical situation.

This, to my mind, is similar enough to drawing an arrow from a quiver, so given that the answer to my first question is that drawing arrows doesn’t count as an item interaction, would the darts example also avoid requiring an item interaction, and if not, why not?

## What is the better use of concentration for a ranged valor bard with elven accuracy, greater invisibility or swift quiver?

Assumptions:

• the bard has 20 dex
• the bard is shooting with a longbow
• another player can consistently provide the help action for 1 attack with advantage every turn
• the bard has elven accuracy

The bard is level 10, so a +4 proficiency. The bonus action would generally be used to either cast Healing Word on allies or give them bardic inspiration. For the sake of this question, we can just look at raw damage

So the comparison as I understand it is:

Greater Invisibility: 2 attacks with Elven accuracy advantage, bonus action available

Swift Quiver: 4 attacks, 1 with Elven accuracy advantage, no bonus action available

## Could Swift Quiver provide silvered/adamantine ammunition?

As I understand it, silvered (PHB p. 148) and/or adamantine (XGtE p. 78) weapons or ammunition do not automatically count as magical. There is no text describing them as magical, and they are not found on lists of magic items (unlike, for example, Mithral Armor or Adamantine Armor which appear on a list of magic items in the DMG).

I mention this because the spell Swift Quiver has some text that concerning nonmagical ammunition (PHB, p. 279-280, bold added):

Components: V, S, M (a quiver containing at least one piece of ammunition)

You transmute your quiver so it produces an endless supply of nonmagical ammunition…

Each time you make such a ranged attack, your quiver magically replaces the piece of ammunition you used with a similar piece of nonmagical ammunition.

So the ammunition that is produced by this spell is nonmagical, but otherwise is “similar” to whatever piece of ammunition was just used. And the quiver starts with at least one piece of real ammunition in it (that you used as part of a material component to cast the spell, and that is not consumed in the casting). So that got me thinking:

If someone was to have a quiver that contained one silvered arrow and one adamantine coated arrow (neither of which was magical), would they then be able to use Swift Quiver to attack with silvered (or adamantine) arrows until the end of the spell’s duration?

## Sufficient conditions for (pointed) quiver representations to be “nondegenerate”

I am interested in the following problem. Suppose we have a quiver $$Q$$, together with a quiver representation $$V$$ of $$Q$$. Let us say that, at each vertex $$p \in Q_0$$, we choose an element $$\alpha_p \in V^*_p$$, where $$V_p^*$$ is the dual space of $$V_p$$. Let us call $$(V, (\alpha_p))$$ a “pointed” quiver representation of $$Q$$.

I am interesting in the following concept. Call $$(V, (\alpha_p))$$ nondegenerate at $$p \in Q_0$$ if the set of all $$f_e^*(\alpha_{p’})$$ is in general linear position, as $$e$$ ranges over all directed edges starting at $$p$$, where $$p’$$ is the endpoint of $$e$$, which of course depends on $$e$$ (and $$f_e$$ is the linear map attached to the edge $$e$$ by the quiver representation). $$(V, (\alpha_p))$$ is said to be nondegenerate if it is nondegenerate at all $$p \in Q_0$$.

I am interested in finding sufficient conditions for a pointed quiver representation to be non-degenerate.

Has this concept been studied before? If so, can someone point me to the right locations in the literature? If not, does anyone have any idea how to find such (non-trivial) sufficient conditions?

## Sufficient conditions for (pointed) quiver representations to be “nondegenerate”

I am interested in the following problem. Suppose we have a quiver $$Q$$, together with a quiver representation $$V$$ of $$Q$$. Let us say that, at each vertex $$p \in Q_0$$, we choose an element $$\alpha_p \in V^*_p$$, where $$V_p^*$$ is the dual space of $$V_p$$. Let us call $$(V, (\alpha_p))$$ a “pointed” quiver representation of $$Q$$.

I am interesting in the following concept. Call $$(V, (\alpha_p))$$ nondegenerate at $$p \in Q_0$$ if the set of all $$f_e^*(\alpha_{p’})$$ is in general linear position, as $$e$$ ranges over all directed edges starting at $$p$$, where $$p’$$ is the endpoint of $$e$$, which of course depends on $$e$$ (and $$f_e$$ is the linear map attached to the edge $$e$$ by the quiver representation). $$(V, (\alpha_p))$$ is said to be nondegenerate if it is nondegenerate at all $$p \in Q_0$$.

I am interested in finding sufficient conditions for a pointed quiver representation to be non-degenerate.

Has this concept been studied before? If so, can someone point me to the right locations in the literature? If not, does anyone have any idea how to find such (non-trivial) sufficient conditions?

## Quiver algebra not derived equivalent to its opposite algebra

Let $$A=KQ/I$$ be a quiver algebra with the following two properties:

a)Q is an acyclic quiver

b) the injective envelope of $$A$$ is projective.

Question 1: Is there an algebra $$A$$ with properties a) and b) such that $$A$$ is not derived equivalent to its opposite algebra $$A^{op}$$?

(in case you know easy examples it would also be interesting to see an algebra $$A$$ not derived equivalent to $$A^{op}$$ with just property a) or b))

Question 2: Is every Nakayama algebra $$A$$ derived equivalent to $$A^{op}$$?

Note that by https://www.sciencedirect.com/science/article/pii/S0021869315000575, at least the singularity categories are equivalent.

## Core of the Jordan quiver variety

It is known that, given the Jordan quiver, dimension vectors $$\textbf{v}=n,\textbf{w}=1$$ and a stability condition $$\theta<0,$$ the corresponding quiver variety $$\mathcal{M}_{\theta}(n,1)\cong \text{Hilb}^n(\mathbb{C}^2)$$ is isomorphic to the Hilbert scheme of n points on $$\mathbb{C}^2.$$ Furthermore, the canonical morphism $$\pi:\mathcal{M}_{\theta}(n,1)\rightarrow \mathcal{M}_{0}(n,1)$$ is identified with the Hilbert Chow morphism $$\text{Hilb}^n(\mathbb{C}^2)\rightarrow Sym^n(\mathbb{C}^2).$$ Under this morphism, the central fiber (also called the punctual Hibert scheme) $$\Lambda=\pi^{-1}(0)$$ is known to be
1. Irreducible
2. Smooth for $$n=2$$ and singular for $$n\geq 3$$
3. Of complex dimension $$n-1={1\over 2} dim(\mathcal{M}_{\theta}(n,1))-1$$
The question is, whether any of 1-3 is known for Jordan quiver varieties $$\mathcal{M}_{\theta}(n,r)$$ with framing $$\mathbf{w}=r,r>1$$ (also known as Gieseker moduli spaces)?

## Does Swift Quiver end early if you run out of arrows after being cast?

The 5th level ranger spell swift quiver (PHB, pp. 279-280) says (bold italics emphasis mine):

Components: V, S, M (a quiver containing at least one piece of ammunition)

You transmute your quiver so it produces an endless supply of nonmagical ammunition…

On each of your turns until the spell ends, you can use a bonus action to make two attacks with a weapon that uses ammunition from the quiver. Each time you make such a ranged attack, your quiver magically replaces the piece of ammunition you used with a similar piece of non magical ammunition.

The way I read this, the ammunition is replaced only when you use it to make these special bonus action attacks, and will not replace ammunition that you use when you make regular attacks with your action.

So, let’s say we have a ranger who has only one arrow left. They cast swift quiver (the quiver containing only one piece of ammunition satisfies the material component requirement) and now that spell is active.

If that ranger fires their last arrow with their action (i.e. a “regular” attack, not one of these arrow-replacing bonus action attacks), would the spell end because the quiver no longer contains any ammunition (and given my reading that the spell doesn’t replace ammunition used up by “regular” attacks)? Or is it that, because the material component was satisfied at time of casting, the material component doesn’t need to remain valid for the duration of the spell after that point?