Learn Spanish (Latin America): Ayer había insectos con antenas muy largas. - Yesterday there were insects with very long antennas.

When haber is used impersonally to mean 'there were' in the past, standard Spanish requires it to remain in the singular form (había). It acts as a fixed expression rather than a normal verb with a subject. While you will frequently hear native speakers in Latin America casually say habían insectos, formal grammar enforces había for both singular and plural objects.

The sentence starts with the specific timeframe ayer, so why use the imperfect había instead of the preterite hubo?

We use the imperfect había because it describes a state or sets a scene in the past, merely stating what existed. The preterite hubo is reserved for specific events that took place or happened, like ayer hubo una tormenta (yesterday there was a storm). Even with ayer, the physical existence of the insects is treated as descriptive background information, not a completed event.

If I wanted to say the insects had long antennas instead of there were insects, would the verb still be singular?

No, in that case, the insects become the active subject of the sentence, so the verb must be plural. You would use the verb tener and conjugate it to match the plural subject: los insectos tenían antenas muy largas. The singular-only rule is unique to impersonal haber.

How do we know structurally that largas describes the antennas and not the insects?