Math 747, Spring 2009, Professor Kustin

Announcements

• Here are my Macaulay2 calculations for example 4.20 on page 66 in Hassett. This is the example about the secants of the twisted cubic. Here is a second approach to the same problem. The calculations are much more simple.
• Here are my Macaulay2 calculations for something close to exercise 4.12 on page 71 in Hassett. This is the example about ``TwoScrollsHaveTheSameIdealMarch-3-2009''.
  
  
• A running list of Typos in Hassett.
  
  
• If you are interested, Tatiana found a preliminary copy of Hassett's book on the web.

Course Announcement and References

• Course Announcement: Math 747, Spring 2009. The course announcement also serves as the syllabus.
• References: .pdf format or .ps format

Homework

• Homework 8: .pdf format or .ps format. This homework is due not too much after the last day of class.
  
  
• Homework 7: This homework is due at the beginning of class on Wednesday, April 15, 2009. There are four problems: 6.6, 6.11, and 6.14 from Hassett and compute a generating set for the intersection of the ideals (x_1,x_2,x_3)^* and (x,3,x_4,x_5-1)^* in the polynomial ring k[x_1,...,x_5]. You are welcome to remember that we made this calculation on page 49 in Hassett (and we corrected the typo which appears there.) ^* OOPS. I MADE TWO TYPOs: (x_1,x_2,x_3) is supposed to be (x_1,x_2,x_5) and (x,3,x_4,x_5-1) IS SUPPOSED TO BE (x_3,x_4,x_5-1).
  
  
• Homework 6: .pdf format or .ps format. This homework is due at the beginning of class on Wednesday, April 1, 2009.
  
  
• Homework 5: .pdf format or .ps format. This homework is due at the beginning of class on Wednesday, March 18, 2009.
  
  
• Homework 4: .pdf format or .ps format. This homework is due at the beginning of class on Wednesday, February 18, 2009.
  
  
• Homework 3: .pdf format or .ps format. This homework is due at the beginning of class on Monday, February 9, 2009. This is the entire assignment. I had Macaulay2 do problems 9 and 10 in Hassett. I'll post these solutions when you are ready. If nothing else, it will show you which M2 commands I used.
  
  
• Homework 2: .pdf format or .ps format. This homework is due at the beginning of class on Wednesday, January 28, 2009. This is the entire assignment.
  
  
• Homework 1: .pdf format or .ps format. This homework is due at the beginning of class on Wednesday, January 21, 2009. By the way, Brett Barwick pointed out that the map phi in problem 1.11b is clearly not a k-algebra homomorphism, here the author has to mean phi* instead. Also, Andrew Vincent and Ser-Wei Fu were not happy with the parameterization in #4 of Example 1.9 in the text book. They looked up the parameterization on Noam Elkies' homepage and found that our book is missing a minus sign. The line
  y_0 = (u_2 + u_1) ... should read
  y_0 = -(u_2 + u_1) ...