Byggingarúrgangurinn og grófi úrgangurinn eru hér.

Because the subject is made of two things joined by og: byggingarúrgangurinn and grófi úrgangurinn. Each one is singular by itself, but together they form a plural subject, so Icelandic uses the plural verb eru.

Compare:

• Úrgangurinn er hér. = The waste is here.
• Úrgangurinn og ruslið eru hér. = The waste and the trash are here.

It is the suffixed definite article, which often corresponds to English the.

So:

• úrgangur = waste
• úrgangurinn = the waste

The same happens in the compound:

• byggingarúrgangur = construction waste
• byggingarúrgangurinn = the construction waste

In Icelandic, the article is very often attached to the end of the noun instead of being a separate word.

Because the adjective is modifying a definite noun. In Icelandic, when an adjective comes before a definite noun, the adjective usually takes the weak form.

So:

• grófur úrgangur = coarse/bulky waste
• grófi úrgangurinn = the coarse/bulky waste

Here úrgangurinn is masculine singular nominative definite, so the adjective appears as grófi, the matching weak form.

Because Icelandic makes very heavy use of compound nouns. What English often writes as two words, Icelandic often writes as one.

So byggingarúrgangurinn is built from:

• byggingar- = building/construction-related
• úrgangur = waste
• -inn / -urinn = the

The whole thing acts as a single noun, so the definite article is added at the very end of the compound.

It is singular. The head noun is úrgangur, which is singular here, and the definite ending shows that as well.

The first part, byggingar-, does not make the whole word plural. It is just the modifying part of the compound. So the sentence has two singular noun phrases, and that is why the verb becomes plural only because they are joined by og.

They are in the nominative case, because they are the subject of the verb eru.

You can see that in forms like:

• úrgangurinn = nominative singular definite
• grófi úrgangurinn = nominative singular definite with a weak adjective

If this noun phrase were an object instead, the forms would change. For example, a direct object might appear as úrganginn rather than úrgangurinn.

Because these are being treated as two separate noun phrases:

• byggingarúrgangurinn
• grófi úrgangurinn

Repeating úrgangurinn makes the structure clear and natural: one kind of waste and another kind of waste. Icelandic can sometimes leave out a repeated noun when the context is very clear, but in a sentence like this, repeating it is the normal and easiest way to say it.

Hér means here and indicates location.

In this sentence, eru hér means are here. The sentence can also be rearranged in natural Icelandic:

• Byggingarúrgangurinn og grófi úrgangurinn eru hér.
• Hér eru byggingarúrgangurinn og grófi úrgangurinn.

Both are possible. If hér comes first, the verb usually comes right after it because Icelandic follows a verb-second pattern in main clauses.

Because Icelandic normally does not need a separate word like English the in this kind of phrase. Definiteness is usually shown by the ending on the noun, and the adjective changes form to match it.

So English uses:

• the bulky waste

But Icelandic uses:

• grófi úrgangurinn

The noun carries the definiteness, and the adjective shows it by taking the weak form.