Ohhhhhhhhhhhhh fuuuuuuuck THE IMPOSTOR. IT'S COMING. GET IN THE GOD DAMN KART, MARIO. NOW NOW NOW NOW.


Yahoo!


Alright, let's put the pedal to the medal, GO, GO, GO, GO. ZOOOOOOOOOOOOM ZOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOM

Waha! I'm-a faggot. Yaha!

Alright, Mario give me your energy and let's outrun the impostor!

Yahoo! Look-a at my faggot mustache!

Sorry, Mario, I have to concentrate on the road. Wait, an item box. Let's get it *Cling* What's it gonna be, what's it gonna be?

Ring-a-ling. Ring-a-ling.

.

.


FUCK. A useless fucking banana peel. Mario, just take that shit and throw it in the middle of the road like it's dogshit.

Wahoo! See-a you later-a dog-a-shit!

Fuck, fuck, fuck, he's gaining on us. The damn impostor is shooting fireballs at us. FUCK FUCK FUCK FUCK FUCK.

Wahoo! I'm-a big-a fuckin faggot! I love-a sucking-a a cock! I-a love-a sticking-a my big-a Italian cock-a into tight-a boy-a-pussy. I-a love-a turning little faggots into-a cock-a-sluts!

FUCK FUCK FUCK, he's REALLY gaining on us. The god DAMN impostor is too fast! He's jumping on koopas and shooting shells at us and I'm barely dodging them! What do I do!? Oh, shit! There's another item box! *Cling* Oh shit what's it gonna be?

Ring-a-ling, ring-a-ling.

.

.


NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.

I'm-a big-a gay-a faggot-a. Why-a is-a Chris-a Pratt-a play-a-ing me-a in the-a new-a movie-a if-a he's-a straight-a.

THROW THIS WORTHLESS SHIT INTO THE ROAD AGAIN, MARIO. FUCK, FUCK, FUCK. HE'S ON ME. HE'S GOT ME BY THE TAIL.

I'd-a dress-a you-a up-a in-a Tanuki suit-a and grab-a your furry tail-a while I-a pound-a you in-a the boy-a-pussy.

Another item box! Oh boy, motherfuckers! Here we go! Cross your god damn fingers, Mario.

I'll-a cross-a my-a fat-a-fingers and spread-a your-a tight-a virgin-a butthole-a with it.

Ring-a-ling, ring-a-ling.

.

.

.


AWWWWWWWWWWWWWWWWWWWWWWWWWW YES, STARRRRRRRR POWERRRRRRRR BITCHES. LET'S GET FUNKY.

I'm-a huge-a fucking faggot. I've-a fucked-a every-a Toad-a in-a the-a whole-a god-a-damn castle. When I-a save-a Toad-a, and the Toad-a is-a like-a "Sorry-a, Mario-a you're-a princess-a is-a in-a-nother castle," I'm-a like-a "Not-a quite-a Toad-a. When I'm-a done-a with you, you'll-a be-a princess-all-a-right-a."

IMPOSTOR: GETTING ON MY TAIL WAS YOUR BIGGEST MISTAKE. TAKE THIS.

BANG.

.

.

. Hah. Gottem. *Parks kart*. Now let's unmask this damn motherfucker like Scooby-Doo, and figure out who was behind all this. *Unmasks impostor*




Wahoo! We-a have-a you-a cornered, bitch!

What!? Mario? You're a double agent!? Wait... So the "Mario" behind me, is...?


Heh.... Or should I say, "Yahoo"?

YOU'RE THE IMPOSTOR?

Tsk, tsk, you never learn, holeinmyheart.

I should have known the impostor was a faggot.

...That's not what I meant.

You hired Mario as a goon? FUCK YOU, IMPOSTOR. ALL MY PLANS ARE RUINED BECAUSE OF YOU.

Idiot. Your panic, your lack of critical thinking, your rashness, your incompetence. That's what led to your demise. Don't blame me.

So, what are you gonna do now, huh, Imposter? Infect me with your god damn impostor syndrome?

Hah! What are you talking about, fool? Imposter syndrome is for hardworking people that have achieved measurable success, yet still feel out of place. You haven't achieved measurable success. You've measurably underperformed in every position you've ever been placed in. You know that acronymn, for goal setting: SMART? Specific, Measurable, Achievable, Relevant, Time-Bound. Well, you've failed in every category. You've SMARTly failed. Why are you even driving a Kart? You are an impostor. Your impostor syndrome is fake.

Damn! I even impostored the impostor syndrome!?

Lol.

But Amogus, all this self-doubt, even if it's accurate, is so debilitating! Even if I know all my problems are my own fault, I have to blame them on something so as to keep moving.

Hah! Your "self-doubt" only exists due to the fact that you're thinking about yourself rather than the things you should be doing. You should be fixing your problems, not ruminating over them.

Damn, Amogus. That's deep.

BTW: You know what you're the biggest impostor at?

Oh shi–

MATHEMATICIAN.



ANNNNNNND hello reader. I am considering this season finale. There are 3 more exercises left in this section, but I am... not interested in this section (I mean... It's titled "Intersections in Projective Space", which on top of being boring is also not very fundamental anyway I'm guessing).

O, and section 8 has no exercises. But I'll make a post for it anyway: Tomorrow's post will be the last post of chapter 1. It's been almost a year. over 90 posts on this fucking blog. IDK what to write. what do YOU think? Maybe it's finally time for a bit of retrospective or something? after tmrw and I'll prolly take a month or two break from alg geo before resuming chapter 2 (...well i have to decide if I'm gonna continue this insanity).

ANYWAY, today's exercise, as usual, has some UPS and DOWNS. check it out:

A

 

Here's 5.3. and.... honestly I think this part is trivial. You can translate points in P² with a linear transformation, hence maintaining degree. So if you care about a point (x,y, 1), you can translate it to (0, 0, 1), look at the open affine z≠0 and, yea, the resulting poly loses degree, so its multiplicity is going to be less than d. "Ummm, what if there's no z's in the translated poly. Then the resulting degree is d which is indeed ≥ d". Fuck. Maybe not as "trivial" as I originally thought. UPDATE: figured it out. I was tempted to say EXERCISE LEFT 2 READER, butguess since is SEASON FINALE, I might as well go the distance. OK. Let's say our curve is Y = Z(f), and we're looking at the point P = (p_x,p_y, 1). Then we want to translate P to (0, 0, 1), which can be accomplished with the linear transformation

Though recall, to get an equation for the translated curve, we apply the inverse transformation on the variables of the curve equation. So we need

Applied to f, we get

h(x,y,z)	= f(x + pxz,y + pyz,z)
	= cocks + f(pxz,pyz,z)

"cocks" consists of a bunch of terms that have xs and ys in them. Some of them even have zs, which sp00ked me for a bit, but here's the point: The point is that I am a fucking retard. I thought I was going somewhere with this, but I realized that I haven't accomplished anything. I am a fucking idiotic motherfucking. FUCK. I fcking SUCK. Well, ummm, EXERCISE LEFT TO READER LOLOLOLOLOLOLOLOLOLOLOLOOLOL

B

 

Here's 6.1

Letting Y = Z(f), let's assume without loss of generality that P = (0, 0, 1). Then in the set z≠0, we get the curve

0

= gd-1(x,y) + gd(x,y)

where deg g_i = i. I.E. f(x,y,z) = g_d-1(x,y)z + g_d(x,y).

That's as far as I got, and then I had to look at the solution and hate myself forgetting BLOWUP as a way of producing birational equivalence.

HOWEVER: I actually just now, as I was fucking typing this, came up with another clever way to do this. OK, using my "I.E." above:

f(x,y,z)

= gd-1(x,y)z + gd(x,y)

This time, let's look in the open affine x≠0, yielding the A² curve

0

= gd-1(1,y)z + gd(1,y)

which I'll just rewrite as

0

= h1(y)z + h2(y)

(1)

You know it's funny. Even before looking at the solution, I instinctually solved for z in this equation:

z

= -h2(y)∕h1(y)

And I stared at this, and did not realize the significance of what I had done. But if you think about it, THIS IS THE ANSWER. (and I did it without blowing up like in the solution). Denote the curve (1) as X (which is open in Y ). Then consider the following map:

y

(y,-h2(y)∕h1(y))

This is "CLEARLY" an isomophism from an open set of A¹ (i.e. h₁(y)≠0) to X. and we're DUN.

also: STAR POWER (volume alert for the last second)

LAST POST OF CHAPTER 1 TOMORROW. SEEYA THEN.