セミナー -- Algebraic Geometry Seminar

談話会/Colloquium


Title

Old and recent topics on the subject of resolution of singularities

Date

2011年6月29日(水) 16:30〜17:30   (16:00より1階ロビーでtea)

Place

京都大学数理解析研究所 (RIMS) 110 号室

Speaker

Kenji Matsuki 氏 (京大・数理研 & Purdue University)

Abstract

[pdf]

談話会/Colloquium


Title

Toward birational classification of three dimensional algebraic varieties

Date

2011年6月8日(水) 16:30〜17:30  (16:00より1階ロビーでtea)

Place

京都大学数理解析研究所 (RIMS) 110 号室

Speaker

Jungkai Chen氏(京大・数理研 & Taiwan National University)

Abstract

   The major goals of birational geometry are to find a good model inside a birational equivalency class and to study the geometry of such a model. Therefore, it consists of two major parts: the minimal model program and the geometry of minimal models and Mori fiber spaces.
   The purpose of this talk is to give a brief introduction and survey of my recent work with Meng Chen and Christopher Hacon on the birational geometry of threefolds.

RIMS Thursday seminar:

Date: June 9, 2011, 3pm
Place: Room 204, RIMS, Kyoto University
Speaker: Keiji Oguiso (Osaka U.)
Title: Group of automorphisms of Wheler type on Calabi-Yau manifolds and compact hyperkaehler manifolds
Abstract: Wehler pointed out, without proof, that a K3 surface defined by polynomial of multi-degree (2,2,2) in the product of three projective lines admits a biholomorphic group action of the free product of three cyclic groups of order two. I would like to first explain one proof of his result and in which aspects his example is interesting. Then I would like to give a "fake" generalization for Calabi-Yau manifolds and explain why it is fake in connection with a result of Professor Kollár. Finally I would like to give a right generalization for Calabi-Yau manifolds of any even dimensions and for compact hyperkähler manfolds particularly of dimension 4 generalizing a construction of Beauville.

RIMS Thursday seminar:

Date: June 2, 2011, 10:30--13:00(small break in the middle 11:40--11:50)
Place: Room 204, RIMS, Kyoto University
Speaker: Sergey Galkin (IPMU)
Title: Mirrors for Mori and Mukai
Abstract: There are only finitely many deformation classes of Fano manifolds in any given dimension, and the list of threefolds is known thanks to Fano, Iskovskikh, Mori and Mukai. Based on ideas from mirror symmetry, we develop an algorithm to list Fano varieties in any given dimension, in particular we were able to recover the known classification of 3-folds. Besides we provide explicit descriptions for Fano threefolds as ("unabelianizations" of) complete intersections in toric manifolds, and thus we compute their Gromov-Witten invariants and prove the mirror symmetry hypothesis. It is a report on the joint project "Fano Varieties and Extremal Laurent Polynomials" with T.Coates, A.Corti, V.Golyshev and A.Kasprzyk (http://coates.ma.ic.ac.uk/fanosearch). I'll review some amusing corollaries of this work, along with further observations and speculations on the next day.
Date: June 2, 2011, 2pm
Place: Room 204, RIMS, Kyoto University
Speaker: Stefan Helmke (RIMS, Kyoto)
Title: Holomorphic loop groups and simple elliptic singularities of degree 5 and 6
Abstract: It is well known that the semi-universal deformation of a simple singularity can be constructed from the adjoint quotient map of the corresponding simple algebraic group. In the same way, the semi-universal deformation of a simple elliptic singularity of degree <5 can be constructed from the adjoint quotient map of the corresponding holomorphic loop group. Since the adjoint quotient is a complete intersection, but the simple elliptic singularities of higher degree are not, the construction seems to fail for those singularities. However, there is a natural modification of the original construction, which can overcome this problem in the case of simple elliptic singularities of degree 5 and 6.

RIMS Thursday seminar:

Date: May 19, 2011, 14:00--15:30
Place: Room 110, RIMS, Kyoto University
Speaker: János Kollár (Princeton U.)
Title: Universal covers of algebraic varieties
Abstract: For an \'etale double cover of smooth curves, the Prym variety is essentially the ``difference'' between the jacobians of the two curves. The Torelli problem for the Prym map asks when two double covers have the same Prym variety. It is known that the Prym map from the moduli space of double covers of curves of genus g at least 7 to principally polarized abelian varieties of dimension g-1 is generically injective. Counter-examples to the injectivity of the Prym map were, up to now, given by Donagi's tetragonal construction and by Verra's construction for plane sextics. It was asked by Lange and Sernesi whether all counter-examples are obtained from double covers of curves of Clifford index at most 3. I will discuss counter-examples to this constructed by myself and Herbert Lange.

〜2010

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