Research on algebraic varieties defined over an algebracally closed field in positive characteristic

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540046
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hiroshima City University
• Principal Investigator: Saito Natsuo 広島市立大学, 情報科学研究科, 講師 (70382372)
• Co-Investigator(Renkei-kenkyūsha): ITO Hiroyuki 東京理科大学, 理工学部, 教授 (60232469)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 正標数 / 代数多様体 / del Pezzo曲面 / F分裂性

Outline of Final Research Achievements

We study the F-splitting of smooth del Pezzo surfaces defined over an algebraically closed field in positive characteristic. We investigate del Pezzo surfaces of degree 2, and gives characterizations of non-F-split del Pezzo surfaces, which exist only in characteristic 2 or 3. In particular, we show that non-F-split del Pezzo surfaces of degree 2 are uniquely determined if the characteristic is 3. Moreover, we determine completely the configuration of 7 points on the projective plane, which are the center of the blow-ups to obtain the non-F-split del Pezzo surface of degree 2 in characteristic 3.

Free Research Field

代数幾何学