- Title: Birational geometry of compactified spaces of rational curves in P²
- Speaker : Kiryong Chung(KIAS)
- Date & Time : Mar 23(Fri) , 2012 2:00~3:00 PM
- Place : Math Science building room 404
: By definition, the Severi variety , which is a quasi-projective variety, is the parameter space of reduced and irreducible planar rational curves of degree with only nodal singularities. As compactifications of , one can consider stable maps space , stable sheaves space and stable pairs space , which are the closures of in the corresponding moduli spaces. In essential, these compactifications arises by focusing the normalization map of planar rational curve. In the viewpoint of birational geometry, it is quite natural to ask the birational relation among these spaces , and . In this talk, I will briefly present the relations (in the sense of Log Minimal Model Program(LMMP)) among these spaces for , which was studied by D. Chen and I. Coskun. As an initial step to run the LMMP for , I will discuss about geometries of and , where the delicate issue is to understand the variation of stable pairs space (in the sense of geometric invariant theory).