Topics in Algebraic Geometry: Aspects of the Cremona Group of the Complex Plane
1.
Review of the Theory of Complex Surfaces: Intersection Product; Linear Systems; Castelnuovo’s Contractibility Theorem; Rational Surfaces.
Review of the Theory of Complex Surfaces: Intersection Product; Linear Systems; Castelnuovo’s Contractibility Theorem; Rational Surfaces.
2. de Jonquières Transformations; Noether-Castelnuovo Theorem.
3. Cantat-Lamy Theorem (non-simplicity of the Cremona group).
References
BEAUVILLE, A. – Complex Algebraic Surfaces (London Mathematical Society Student Texts). Cambridge University Press, 1996.
CANTAT, SERGE,& LAMY, STÉPHANE (2010). – Normal subgroups in the Cremona group. Acta Mathematica. 210 (2013): 31–94.
DOLGACHEV, IGOR V. – Classical Algebraic Geometry: a modern view. Cambridge University Press, 2012.
HUDSON, HILDA PHOEBE. – Cremona transformations in plane and space. Cambridge University Press, 1927.
KOLLÁR, J., SMITH, K., & CORTI, A. – Rational and Nearly Rational Varieties (Cambridge Studies in Advanced Mathematics). Cambridge University Press, 2004.
BEAUVILLE, A. – Complex Algebraic Surfaces (London Mathematical Society Student Texts). Cambridge University Press, 1996.
CANTAT, SERGE,& LAMY, STÉPHANE (2010). – Normal subgroups in the Cremona group. Acta Mathematica. 210 (2013): 31–94.
DOLGACHEV, IGOR V. – Classical Algebraic Geometry: a modern view. Cambridge University Press, 2012.
HUDSON, HILDA PHOEBE. – Cremona transformations in plane and space. Cambridge University Press, 1927.
KOLLÁR, J., SMITH, K., & CORTI, A. – Rational and Nearly Rational Varieties (Cambridge Studies in Advanced Mathematics). Cambridge University Press, 2004.
