Reference no: EM131084041
Math 176: Algebraic Geometry, Fall 2014- Assignment 7
1. Consider V(yz - x2) in P2. What type of conic does this algebraic set look like in the 3 natural affine sections of P2 (i.e. in U0, U1, U2)? What are the points at infinity (i.e. the points where z = 0)?
2. Let V = V(x0x2 - x3x4, x20x3 - x1x22) ⊂ P4. Find equations for the affine algebraic sets V ∩ U0 and V ∩ U3. Are these varieties?
3. Determine, with justification, if the following statements are true or false. Again we assume k is an algebraically closed field with characteristic 0.
(a) A homogeneous prime ideal is radical.
(b) Ia(C(V)) = I(V) for any projective variety V ⊂ Pn.
4. If Y ⊂ An is an algebraic set, recall the Zariski closure is the smallest algebraic set in An containing Υ. We saw on the midterm that this is V(I(Υ)). What is a natural candidate for the projective closure of Υ? Justify why your choice of definition for projective closure is reasonable.
|
Easy to derive an upper bound
: In communication systems, the error probability P[E] may be difficult to calculate; however it may be easy to derive an upper bound of the form P[E] ≤ . In this case, we may still want to estimate P[E] using the relative frequency n(E) of E in n t..
|
|
What force(s) does the forearm exert on the humerus
: What force must the biceps generate to hold the forearm in static equilibrium?
|
|
Determining the total pressure
: Oxygen gas (PO2 = .910 atm), helium gas (PHe = 1.24 atm), and carbon dioxide gas occupy the same container with a total pressure of 2.84 atm. What is the PCO2?
|
|
Relative frequency of a over n independent trials
: When we perform an experiment, event A occurs with probability P[A] = 0.01. In this problem, we estimate P[A] using (A), the relative frequency of A over n independent trials
|
|
Find equations for the affine algebraic sets
: Math 176: Algebraic Geometry, Fall 2014- Assignment 7. Let V = V(x0x2 - x3x4, x20x3 - x1x22) ⊂ P4. Find equations for the affine algebraic sets V ∩ U0 and V ∩ U3. Are these varieties
|
|
Find the fahrenheit temperatures
: Apply the graph obtained in part (c) to estimate visually the Fahrenheit temperature corresponding to a Celsius temperature of 28o. Then calculate that temperature exactly by using the linear equation y = 32 + 1.8x.
|
|
Distinguish between different types of risk
: Comprehensively discuss the main financial risk management tools and techniques. Distinguish between different types of risk and the steps involved in the financial risk management process.
|
|
What is the concentration of h2so4 in the following units
: What is the concentration of H2SO4 in the following units:
|
|
Problem regarding the vibrational frequency
: For HCl represented as a harmonic oscillator, it has a vibrational frequency of 2885 cm-1. The vibrational frequency of DCl (where D is twice the mass of H) should be (assuming HCl and DCl have the same force constant):
|