I am about to go into a battle against some undead and for the first time I've encountered a ghost amongst them. I know that ghosts are only affected by magic, but does that include fire arrows? The only unit I have with anything resembling magic (hero has all healing spells) is an archer with 2x fire arrows.

Not quite sure right now, but I think so. But they can also be killed by units with armorpiercing and attack above 10 (or 20 for ranged), or just by units with melee attack above 20, like Griffons for example. They are usually no problem for high level warriors and scouts.

thats not quite right - ghosts have 20 a defense and 40 randed defense so you would need a ranged attack above or near 40 and then armor piercing shots
fire arrows might work but you should consider that ghosts have 4 or 6 resistance (higher level ghosts tend to have a higher resistance)
so the best way to get rid of them is with an high level warrior (above 20) that has some decent equipment - a mage (one lightning should take care of them maybe two - ghosts have 20hp on expert i think - and 10 on beginner)
or a commander with rank three melee units (knights) or healers (clerics) - the knight is strong enough to damage them in melee and the magicshot from the clerics is quite powerful as well
do not engage them with a scout hero unless you have awesome equipment (something like the ethereal crossbow or the flaming bow + fire arrows/renver's arrows) - especially not if you have some weak rank one units with him (bowmen/elves come to mind) i tried this once or twice - even with fire arrows the scout does only 2-5 damage with each attack but drains his stamina resulting in less damage the tier one units can do nothing and get killed - thus restoring the hp of the ghosts (they have soulsucking and get 5 hp restored for every unit killed)
and always remember ghost don't come alone - most of the time they bring an entourage of other undead units (ghouls zombies skellies) and even if you think you can beat one - the game will be nasty and the encounter will have 2 or 3 ghost (happend to me as well and i had to say bye bye to my hero)

I don't think I was wrong, armorpiercing halves the defense, so above 20 attack will be enough to damage ghosts with 40 defense.

Tyvm for the detailed answer, mr.teach. I chickened out of the fight, which was lucky as I hadn't considered multiple ghosts or magic resist or the ghost healing ability. Interesting point about the armor-piercing shots, jamotide. I suppose 21 ranged attack with armor piercing would do 2 damage.

Magic weapon spell(+4 damage, attack becomes magic).

Units with magic damage. (Sometimes I send my tier 1 healer to take on ghost)

units with "Charge strike" (cavalry, pegasus) Damage from it ignores armor completely. So, horde of 0 level horsemen can take on ghost under Invulnerability :)

yeah sorry i just considered precise shots which negates a part of the armor - not armor piercing - but than again you would need a weapon with that ability (every crossbow i think) still on competent (the difficulty i am playing right now) ghost are something i shy away from until i got one uber warrior or a level 20 commander with paladins as level 4 (those are awesome - 2 palas i knight 2 clerics 4 guardsmen and 6 elves are an army to be reckoned with )

Ghosts are not only affected by magic, they have 20 physical resist and 40 ranged resist.
A level 30 ranger with a good crossbow can kill a ghost at full HP with a single double shot. (40/2 = 20 - 7 = 13 adjusted resistance)
And a fighter can handle them much earlier.

That being said, earlier on you want to use magic to kill them. There is a spell which turns a units weapon into magic, this forfeits your armor piercing abilities though.
Magic weapon is very situational so make sure that the math shows it is usesful before casting it, it can often make your attacks weaker.

As Gremlion says. Best way to take down ghosts is with the 2nd level Sorcery Schools Flame Blade Spell.

This works great for your Archer or Warrior especially.

Unless of course your a Mage yourself. Then just take them down with Magic Arrows (x2) if theres only 1 or a Lightning Bolt if your strong enough to 1 shot it when there's multiple.

Maximum level precise strike gives -7 to enemy ranged armor. Where does the 10+ come from? biggest reduction is of-course the halving from using a crossbow.

High level items for scout tend to have this ability too.
Renver's bow have 4, Precise arbalet 2, elven arrows 1, Renver's arrows have +2, Gloves of sniper have 3

Yep, and in my last games I had all of these!!

Ghosts can also be dealt with by using the tier-2 spell "Exorcism".

My scout/archer has learned that spell specifically for dealing with ghosts but the spell also works against a variety of enemies.