I think this is quite good build. The Karthus is extremely squishy by this way but I believe you can handle them (I also tried it and it works.... but I play it another way).
The only thing I don't like in this build is the Mana Potion for start (it gives you almost nothing because Karthus has great mana-pool; 100 mana is almost nothing for him.... I think that you can use Health Potion much better - especially with this squishy build).

It's a nice build but you lack on both hp and Magic pen,try getting magic pen it's a huge difference late game...

Ive added a second build that focuses Rylai's first I think this makes for a much more aggressive build. The only issue i have is end game porting back to heal can be a hassle.

the hat sure is nice for req, for sure. But before level 11 all you have really are your tears and boots, and maybe the blasting wand... that's like critical moments of anything to happen during ur level 6-10 experience. You want some more AP and fast by that time. I usually get my hat around level 16 after I have ROA and Rylai's. It helps to have those 2 first for the time before u get ur hat, and by then peeps die >.>
P.S yah, as I first started out as Karthus I used to never get ROA and I'd just rush Arch, then ryalis and hat. Now I find that having ROA helps me alot in team fights for the extra mana/health/AP and that, my friend, Is just fantastic! Especially if you can get that sucker at 10 minutes, which I usually do :P

RoA is nice for the extra health but thats about it for me if I want the mana tears works better, I think right now im split between Rylais and Death Cap. sure cap is expensive but i get it before lvl 11 and the boost you get for requiem is nice.

I just tried out Rylais as a first item we won and i noticed a drastic change but i will have to try it again several more times before i can say for sure i like it better

Well, as i said that extra damage at the beginning shouldn't be a problem since you barely engage in the beginning. The only time's you do is when you have someone who is over harassing you constantly, and then the flap AP quints are more than enough early dmg to carry you over til end game AP per level runes come into effect.
Also Ryali's as a starter is decent, but i like to either get ROA or Arch as my starter, Just never the hat (I know it's good, but its more of a mid/late game item, Trust me i generally get more AP than the casters who rush rabadon's all the time)

AIVION
your ideas are pretty sound but I suppose the one thing I left out of my build is that my team make up most of the time is lacking on the support. Ive never considered Ryalis as a starter I suppose it would be nice for them to not know your coming when you throw up a wall.

You said AP per lvl? idk about this yes it is more AP in the end but the percents at end game are minimal compared to the benefit of the like 15 extra dmg in the beginning 30 if you hit a single target with Lay Waste. and sure they don't help much late game but those early kills can really help.

Im still deciding if I want WoTA as my final item abyssal used to be my last item but I found alot of my late game kills came from Requiem. If I get rushed late game I tend to die and I dont get the -20 MR from abyssal. I guess I dont get any real help from WoTA but it keeps me from getting ganked often and makes players think twice about attacking me solo when I'm always at full health, especially when the re spawn gets up there like 55 seconds

I thought about he second AA but I do enjoy the ability to be at full health every time I walk by minions. Tonight Ill give second AA another shot though.

hmm... Being an Avid Karthus player for one and a half years, I shall tell you straight! ra!
1! I do not agree with your quintessences. You should focus on one or the other, Especially having a flat health quint? What? As Karthus, you shouldn't have to worry much about getting hit. Usually either full MP quints or flap AP quints or even AP per level are alot better choices IMO. I recommend you start out with a catacylst and work into a ROA instead of getting deathcap first (I see you start with a tear, maybe build into Arch first? Or Ryali's?)... but deathcap first?! Not a good idea at all! You should either get your ryali's (which is core for hard core karhus players) or a Archstaff first(Or if u do it my way, ROA, which i guess is up to you since i never used to get ROA Myself :P) Thats just up to me, do it if you want, just tryin to help.
2! The flat AP glyphs are, yes, up to people and their tastes, but it's not as worth it as AP per level counterparts. The extra AP in the beginning isn't exactly mandatory with Karthus as it is with other casters, like Vlad. It's usually better for jungling. AP per level gives you alot more ap for your ip!
3! WOTA shouldn't really be apart of your core build. It's one of those items that's either useful or not. Like if your the only caster on your team, etc. Don't get me wrong, I loves me my WOTA with Karthus once in a blue moon, and also when I have other AP peeps with me on my team too. I'd rather have my last items be somethin of the defensive proportions, like maybe a banshee's or abyssal for the extra MR? Or maybe another armor item if the teams huge on DPS.
Overall, I like it. Especially the team fight and where Karthus stands in a team fight section... wonder why I never thought of that :P Anyway Hope I helped, and continue playing the best AP person eva!

Woot even the comments are educational , just like the guide/build itself.

+1

QUOTE TUNNEL!
I completely agree on the WoTA logic, but there are just much more viable items on Karthus. At most, I'd sell it late-game (if you ever even get their with karthus, lul) and supplement a heavier AP item.