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NCTS Seminar on Algebraic Geometry
15:30 - 17:00, April 16, 2021 (Friday)
Lecture Hall 5F, Cosmology Building, NTU
(臺灣大學宇宙學大樓 五樓演講廳)
(Part I - Talk 5) Existence of Miniversal Family and Pro-representability
Hsin-Ku Chen (National Taiwan University)


NCTS Algebraic Geometry Learning Seminar will focus on the deformation theory in the first half year. This is 5th talk of Part I.
Part I - Abstract deformation theory. Reference: [Har10]. Pre-requisite: We should assume everyone is familiar with the definition and basic properties of the Hilbert scheme (but not with its construction). If this is not the case, we should recall them during the first talk.
Talk 5 (Chapter III, Sec. 18-20) Conditions for existence of miniversal family/pro-representability of deformation functor of a scheme/sheaf. Abstract deformations vs. embedded deformations.
Part I - Abstract deformation theory. We mainly follow Hartshorne's Deformation Theory book.
Part II - Deformation theory and DGLA. We follow Manetti's note.
Part III - Deformation of rational curves. We follow Debarre's Higher Dimensional Algebraic Geometry.
Part IV - Other related work. To be announced later.


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