Birational Mori fiber structures of Fano varieties and rationality problem

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800019
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Saga University
• Principal Investigator: Okada Takuzo 佐賀大学, 工学(系)研究科(研究院), 准教授 (20547012)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: ファノ多様体 / del Pezzo束 / コニック束 / 有理性問題

Outline of Final Research Achievements

We determined the birational Mori fiber structures of members of 21 families of 3 dimensional Fano weighted complete intersections of codimension 2. Moreover we classified birationally rigid Fano threefolds embedded as a codimension 3 subvariety in a weighted projective space. As a consequence, the classification of birationally rigid Fano threefolds which are embedded as a codimension at most 3 subvariety in a weighted projective space is completed. We also proved the non-rationality of some 3-dimensional del Pezzo fibrations admitting an action of the Klein simple group, and proved K-stability of various birationally rigid Fano threefolds.

Free Research Field

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