Problem Set #4
Due: 4 February 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve.
1. Let I := wy x2 , wz xy, xz y2 Q[x, y, z, w].
(a) Find the reduced
Problem Set #9
Due: 18 March 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve. Solve problems #3, #4, and #5 without
using a computer algebra system.
Problem Set #8
Due: 11 March 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve. Solve problems #2 and #3 without using
a computer algebra system.
1. Th
Problem Set #7
Due: 4 March 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve.
1. In Q[x, y], consider f = x2 y 3xy2 + x2 3xy and g = x3 y + x3 4y2 3y
Problem Set #5
Due: 11 February 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve.
1. Some parametric curves and surfaces are algebraic varieties even
Problem Set #10
Due: 25 March 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve.
1. Let X = V(x3 y4 ) A2 (C).
(a) Show that there is a bijective morphi
Problem Set #11
Due: 1 April 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve. Solve problem #4 without using a
computer algebra system.
1. In this pr
Problem Set #12
Due: 8 April 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve.
1. The general linear group GL(kn+1 ) is the set of invertible (n + 1)
Problem Set #3
Due: 28 January 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve.
1. Suppose that k is an innite eld. Let X A3 (k) be the set X = cfw_(
Problem Set #6
Due: 18 February 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve.
1. Use elimination to solve the system
0 = x2 + 2y2 y 2z
0 = x2 8y2
Problem Set #2
Due: 21 January 2011
Students registered in M ATH 413 should submit solutions to three of the following problems.
Students in M ATH 813 should submit solutions to all ve.
1. (a) Show that X = cfw_(x, x) : x R, x = 1 A2 (R) is not an afne va