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Jun
14
awarded  Popular Question
Jun
5
awarded  Popular Question
May
3
asked Basis for a topology of a scheme
May
3
awarded  Yearling
Apr
28
comment What is a smooth family of divisors?
It is a terminology used by Zariski (or Mumford), for example in the book "Algebraic Surfaces".
Apr
28
asked What is a smooth family of divisors?
Apr
22
awarded  Popular Question
Mar
13
awarded  Nice Question
Mar
5
revised Family of curves with one base point and a blow-ups.
edited body
Mar
4
comment Effective divisor vs curve on surface
@manifold good question! Look at the definition of "curve on a surface" on this web page: amathew.wordpress.com/2013/01/27/… Unfortunately the "equivalence" is not proved.
Mar
4
revised Family of curves with one base point and a blow-ups.
added 26 characters in body
Mar
4
revised Family of curves with one base point and a blow-ups.
added 5 characters in body
Mar
4
asked Family of curves with one base point and a blow-ups.
Mar
1
awarded  Popular Question
Feb
25
awarded  Good Question
Feb
20
comment Rational map on $\mathbb P^1$ and its fibers
I don't understand only the followiing point: "But at least one exceptional curve over each point of indeterminacy must map onto $\mathbb P^1$"
Feb
20
comment Rational map on $\mathbb P^1$ and its fibers
Ok a $(-1)$-curve $E$ can't be mapped to a point of $\mathbb P^1$ since this implies that $E^2=0$... But what about the second question?
Feb
20
comment Rational map on $\mathbb P^1$ and its fibers
Your answer is clear, but I'm intrested to your last comment. Can you give me some extra details about the "second method" to prove the claim? Why each exceptional curve maps onto $\mathbb P^1$? And why this implies that claim?
Feb
18
accepted Rational map on $\mathbb P^1$ and its fibers
Feb
18
comment Rational map on $\mathbb P^1$ and its fibers
Ok the question is the following: In general a fiber $\psi^{-1}(y)$ is closed in $S\setminus\Delta$ but not closed in $S$. In which way can you obtain its closure? By adding only some points of nondefinition?