Math 145, Problem Set 6. Due Friday, May 23.
You may assume that the ground eld is k = C.
1. (Hyperelliptic curves.) Let a1 , . . . , a5 be pairwise distinct constants. Find the singularities of
the p
Math 145, Problem Set 2. Due Friday, April 18.
1. Let X1 , X2 be afne algebraic sets in An . Show that
(i) I (X1 X2 ) = I (X1 ) I (X2 ),
(ii) I (X1 X2 ) = I (X1 ) + I (X2 ).
Show by example that takin
Math 145, Problem Set 3. Due Friday, April 25.
For this problem set, you may assume that the ground eld is k = C.
1. Find the irreducible components of the afne algebraic set x2 yz = xz x = 0 in A3 .
Math 145, Problem Set 4. Due Friday, May 2.
For this problem set, you may assume that the ground eld is k = C.
1. Let f and g be distinct irreducible polynomials in k [X, Y ] of degrees d and e. Show
Math 145, Problem Set 5. Due Friday, May 16.
You may assume that the ground eld is k = C.
1. (Products of afne varieties.) Let X An and Y Am be afne algebraic sets.
(i) Show that X Y An+m is also an a
1984
Essay prompts adapted from AP Literature and Composition prompts.
Choose one. Remember that words like contributes to the meaning of the
work are asking you to discuss the large thematic issues o
Hobos
Hobos are so cool
They swim in a pool
They like and want money
They lick and like honey
Some of their bones are broken
They stole a Chuckie cheese token
if there were no hobos
There would be no
To the Ends of the Earth
Kilian Olen
4/24/2014
January 3rd, 2018
After traveling for about eight hours by plane, and 2 hours by boat I have finally made
it to the station in the North Pole where I wil
1.My Family Life
I live in Davie, Florida with my mom, dad, and little sister. My mom,
Ursula, works with Memorial Hospital and my dad, Olaf, works in Cruise
Planners. My little sister, Sienna, is 11