Algebraic Geometry Seminar

The algebraic geometry seminar in Term 2 2024/2025 will usually meet on Wednesdays at 3pm, though we may sometimes change to allow speakers from other time zones.

Each talk will be either in B3.02 or MB0.07 -- see specific information below.

A link to talks from the previous term is here.

Wednesday 15 January 2025, 3pm. Speaker: Miles Reid (Warwick)

Title: The Tate-Oort group TO_n for n >= 1

Abstract: The cyclic group Z/n as you have never seen it before.

Wednesday 22 January 2025, 3pm. Speaker: Elena Maria Guardo (Università di Catania)

Title: Expecting unexpected hypersurfaces

Abstract: Let X be a reduced subscheme in Pn. We say that X admits an unexpected hypersurface of degree d and multiplicity m if the imposition of having multiplicity m at a general point P fails to impose the expected number of conditions on the linear system of hypersurfaces of degree d containing X. We introduce new methods for studying unexpectedness, such as the use of generic initial ideals and partial elimination ideals to clarify when it can and when it cannot occur. We formulate a new way of quantifying unexpectedness (our AV sequence), which allows us detect the extent to which unexpectedness persists as increases but remains constant. We also study how knowledge of the Hilbert function, together with certain geometric assumptions, can provide information about unexpected hypersurfaces. This is based on the joint paper with G. Favacchio, B, Harbourne, and J. Milgliore.

Wednesday 29 January 2025, 3pm. Speaker: Livia Campo (University of Vienna)

Title: K-stablity of Fano threefold hypersurfaces of index 1

Abstract: The existence of Kaehler-Einstein metrics on Fano 3-folds can be determined by studying lower bounds of stability thresholds. An effective way to verify such bounds is to construct flags of point-curve-surface inside the Fano 3-folds. This approach was initiated by Abban-Zhuang, and allows us to restrict the computation of bounds for stability thresholds only on flags. We employ this machinery to prove K-stability of terminal quasi-smooth Fano 3-fold hypersurfaces. This is deeply intertwined with the geometry of the hypersurfaces: in fact, birational rigidity and superrigidity play a crucial role. The superrigid case had been attacked by Kim-Okada-Won. In this talk I will discuss the K-stability of strictly rigid Fano hypersurfaces via Abban-Zhuang Theory. This is a joint work with Takuzo Okada.

Wednesday 29 January 2025, 4pm. MS.04 Speaker: Taro Sano (Kobe University) (Note unusual time and location!)

Title: Delta invariants of Fano weighted hypersurfaces

Abstract: K-stability (or existence of Kähler-Einstein metrics) of explicit Fano varieties has been studied for a long time. Delta invariants (stability thresholds) detect the K-stability of Fano varieties. Moreover, Abban--Zhuang developed a powerful method to compute the delta invariants by adjunctions. In this talk, I will explain our recent results on the K-stability of some Fano weighted hypersurfaces via the Abban--Zhuang method.

Wednesday 5 February 2025, 3pm. Speaker:

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Wednesday 12 February 2025, 3pm. Speaker:

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Wednesday 19 February 2025, 3pm. Speaker:

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Thursday 20 February 2025.

COW

Wednesday 26 February 2025, 3pm. Speaker:

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Wednesday 5 March 2025, 3pm. Speaker:

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Wednesday 12 March 2025, 3pm. Speaker:

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