The shape of an algebraic variety
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The shape of an algebraic variety 68th Kuwait Foundation Lecture University of Cambridge, November 1st, 2007 Carlos T. Simpson C.N.R.S., Laboratoire J. A. Dieudonne Universite de Nice-Sophia Antipolis
Voir
- mixed hodge
- basic question
- tive malcev completion
- variety over
- topological space
- xtop
- hodge struc- tures
- then xtop ?
- hodge theory
The shape of an algebraic variety
68 th Kuwait Foundation Lecture
University of Cambridge, November 1st, 2007
Carlos T. Simpson
C.N.R.S.,LaboratoireJ.A.Dieudonn´e Universit´edeNice-SophiaAntipolis
Equations ⇒ Topology
X algebraic variety over C
X top associated topological space
( P n ) top = CP n usual complex projective space in topology
If X ⊂ P n C given by equations F i ( Z 0 Z n ) = 0 then X top ⊂ CP n is the closed subspace, same equations, induced topology
Example: X ⊂ P 2 smooth of degree d C X top = compact Riemann surface of genus ( d − 1)( d − 2) g = 2
