Difference between revisions of "Algebraic Geometry - Raul Pandharipande - 2016"
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''Please sign with your name and the date on which you had your exam. If you use this wiki, contribute to it as well or terrible things will happen to you: like finding out there's a video of yourself drunkenly break-dancing.'' | ''Please sign with your name and the date on which you had your exam. If you use this wiki, contribute to it as well or terrible things will happen to you: like finding out there's a video of yourself drunkenly break-dancing.'' | ||
| − | + | == Romainb == | |
He asked the following questions: | He asked the following questions: | ||
Revision as of 16:34, 23 August 2016
Please sign with your name and the date on which you had your exam. If you use this wiki, contribute to it as well or terrible things will happen to you: like finding out there's a video of yourself drunkenly break-dancing.
Romainb
He asked the following questions:
- Question 6 of the list (description of the Plücker embedding of \(Gr(2,4)\) in \(\mathbb{P}^5\) ).
- Is the quadric \( z_{12}z_{34}-z_{13}z_{24}+z_{14}z_{23}=0\) corresponding to \(Gr(2,4)\) in \(\mathbb{P}^5\) smooth?
- Is the Fermat curve \(z_{12}^2+z_{13}^2+z_{14}^2+z_{23}^2+z_{24}^2+z_{34}^2=0\) also isomorphic to \(Gr(2,4)\)? Is it smooth?
- What is the dimension of \(Gr(2,4)\)? What is the dimension of \(Gr(r,n)\)?
Then he gave me two curves \(x^4+y^2=0\) and \(x^4+17y^2=0\) in \( \mathbb{C}^2 \).
- What is the intersection multiplicity at \( (0,0) \)?
- Do they intersect in another point in \( \mathbb{C}^2 \)? In \( \mathbb{P}^2 \)?
- What is Bézout's Theorem?
Then Question 7 of the list i.e. "Is there a nonconstant regular map \( \mathbb{P}^2 \setminus \{p\} \longrightarrow \mathbb{C}^1 \)?"
