2012 Fiscal Year Final Research Report

A study on compactifications of complex affine planes and spaces

Research Project

Project/Area Number	22540051
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Kumamoto University
Principal Investigator	FURUSHIMA Mikio 熊本大学, 大学院・自然科学研究科, 教授 (00165482)
Project Period (FY)	2010 – 2012
Keywords	代数幾何学 / コンパクト化
Research Abstract	(1) Research 1: The boundary of compactification of C^2 into Hirzebruch surfacesconsists of two irreducible components, one of which can have a singularity byL.Brenton. Then I can construct more general examples including the Brenton’ s one. Ialso prove that one of the irreducible components of boundary divisor is a smoothrationa curve. Further , I suggested the possibility of a birational geometric proof of thetheorem by Abyankar-Moh- Suzuki. (2) Research 2: I studied the detail structure of singular Fano threefolds withGorenstein terminal singularities as a compactification of C^2.,especially , applying thetheory of smoothing of Fano threefolds with Gorenstein terminal singularities, I candetermine the detail structure of the known examples of singular Fanocompactifications of C^3..

(6 results)