GTA Seminar: Mondal -- Normal Compactifications of the Complex Plane

Speaker: Dr Pinaki Mondal (Toronto)

Time: Tuesday, Aug. 21, 12NOON--1PM 

Room: Carslaw 707A

Lunch: after the talk (at Taste at Sydney Uni, 
i.e. "Law School Annex Cafe")

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Title: Normal Compactifications of the Complex Plane

Abstract: we describe a newly observed correspondence 
between two well studied objects: planar complex 
algebraic curves with one place at infinity (studied 
e.g. by Abhyankar-Moh (1975), Russell (1980), 
Nakazawa-Oka (1997), Suzuki(1999)) and normal algebraic 
compactifications of the complex plane with one curve 
at infinity (studied e.g. by Kojima (2001), 
Kojima-Takahashi (2009)). This result leads to a 
classification of normal analytic compactifications 
of the complex plane with one curve at infinity, and 
gives an effective criterion for determining when the 
result of contracting certain negative definite rational 
curves from a rational algebraic surface is also algebraic. 
In particular, it gives an effective algorithm to construct 
non-algebraic normal analytic surfaces. 

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Web site for Geometry Seminar is at: 

http://www.maths.usyd.edu.au/u/SemConf/Geometry/index.html