The shape of an algebraic variety

Sophia Antipolis

Description

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

• mixed hodge


• basic question


• tive malcev completion


• variety over


• topological space


• xtop


• hodge struc- tures


• then xtop ?


• hodge theory

Sujets

• Antipolis
• Taylor
• Topological space
• Hodge theory

Informations

• Publié par: pefav
• Nombre de lectures: 10
• Langue: English

Extrait

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