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wu :: forums    riddles    putnam exam (pure math) (Moderators: Icarus, SMQ, Eigenray, Grimbal, towr, william wu)    Curves with Negative self-intersection « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Curves with Negative self-intersection  (Read 780 times) Michael Dagg Senior Riddler     Gender: Posts: 500 Curves with Negative self-intersection   « on: Aug 21st, 2006, 5:56pm » Quote Modify Let   S_k   be smooth projective surface over a field  k  and let  M  be a field extension of   k  such that  k  is algebraically closed in  M.     Show that every irreducible curve on   S_M  with negative   self-intersection is defined over k. « Last Edit: Aug 21st, 2006, 6:01pm by Michael Dagg » IP Logged Regards, Michael Dagg Michael Dagg Senior Riddler     Gender: Posts: 500 Re: Curves with Negative self-intersection   « Reply #1 on: Oct 31st, 2006, 4:40pm » Quote Modify Let me give a hint:   If   K*  be an algebaic closure of  K,  then  for every v  \in  aut(K*/k)   the curve  v(M)  has the same degree and self-intersection as  M:  Hilbert implies   {v(M): v \in Aut(K*/k)}   is finite.     IP Logged Regards, Michael Dagg Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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