Workshop on Hyperkähler Varieties and Related Topics

B109 IBS, Korea, Republic of

Invited Speakers (three one-hour lectures) Ekaterina Amerik (HSE U.) Yoonjoo Kim (Columbia U.) Zhiyuan Li (SCMS, Fudan U.) Keiji Oguiso (U. Tokyo) Abstracts PDF file Schedule March 10 (Monday) 14:00-15:00 Registration 15:00-16:00 Amerik, Lecture I 16:00-16:30 Coffee Break 16:30-17:30 Li, Lecture I 18:00-20:00 Speakers dinner March 11 (Tuesday) 11:00-12:00 Amerik, Lecture II 12:00-14:00 Lunch 14:00-15:00

Lorenzo Barban, General results on C*-actions on projective varieties

B236-1 IBS, Korea, Republic of

    Speaker Lorenzo Barban IBS CCG In this lecture series we aim to describe the rich relation between C*-actions on complex normal projetive varieties and the birational maps among the associated geometric quotients. We will begin this first seminar by explaining a motivating example, called the Atiyah flop. We will then discuss general results

Lorenzo Barban, Geometric Invariant Theory for C*-actions

B236-1 IBS, Korea, Republic of

    Speaker Lorenzo Barban IBS CCG In this second talk, which is the technical core of the lecture series, we describe several tools to study C*-actions on projective varieties, such as the bandwidth, the AMvsFM Lemma, and the pruning of a variety. With this, we will be able to describe the -birational geometry of

Lorenzo Barban, Geometric realization of birational maps among Mori dream spaces

B236-1 IBS, Korea, Republic of

    Speaker Lorenzo Barban IBS CCG Given a birational map ϕ among normal projective varieties, a geometric realization of ϕ is a normal projective C*-variety such that the birational map among geometric quotients parametrizing general orbits coincides with ϕ. Geometric realizations can be thought of as a projective algebraic version of the notion of

Mihai Paun, Positivity of quotients of holomorphic tensor fields (Lecture I)

B236-1 IBS, Korea, Republic of

    Speaker Mihai Paun U. Bayreuth I will present the main results and techniques in the preprint arxiv:2502.02183 (joint with J. Cao). This was motivated by the recent preprint by W. Ou, cf. arXiv:2501.1808 (especially by the algebraicity criteria for foliations on compact Kähler manifolds in this article). The first lecture is dedicated to

Mihai Paun, Positivity of quotients of holomorphic tensor fields (Lecture II)

B236-1 IBS, Korea, Republic of

    Speaker Mihai Paun U. Bayreuth I will present the main results and techniques in the preprint arxiv:2502.02183 (joint with J. Cao). This was motivated by the recent preprint by W. Ou, cf. arXiv:2501.1808 (especially by the algebraicity criteria for foliations on compact Kähler manifolds in this article). The first lecture is dedicated to

Thibaut Delcroix, Weighted Kähler geometry and semisimple principal fibrations (Lecture I)

B236-1 IBS, Korea, Republic of

    Speaker Thibaut Delcroix Université de Montpellier In Kähler geometry, especially in the questions of existence of canonical Kähler metrics, the volume form ωn associated with a Kähler form ω plays a central role. In weighted Kähler geometry, we consider a Kähler manifold X equipped with a Hamiltonian action of a torus T, a

Jinhyung Park, Effective gonality theorem on weight-one syzygies of algebraic curves

B236-1 IBS, Korea, Republic of

    Speaker Jinhyung Park KAIST In 1986, Green-Lazarsfeld raised the gonality conjecture asserting that the gonality gon(C) of a smooth projective curve C of genus g can be read off from weight-one syzygies of a sufficiently positive line bundle L, and also proposed possible least degree of L, that is 2g+gon(C)-1. In 2015, Ein-Lazarsfeld

Thibaut Delcroix, Weighted Kähler geometry and semisimple principal fibrations (Lecture II)

B236-1 IBS, Korea, Republic of

    Speaker Thibaut Delcroix Université de Montpellier In Kähler geometry, especially in the questions of existence of canonical Kähler metrics, the volume form ωn associated with a Kähler form ω plays a central role. In weighted Kähler geometry, we consider a Kähler manifold X equipped with a Hamiltonian action of a torus T, a

Thibaut Delcroix, Weighted Kähler geometry and semisimple principal fibrations (Lecture III)

B236-1 IBS, Korea, Republic of

    Speaker Thibaut Delcroix Université de Montpellier In Kähler geometry, especially in the questions of existence of canonical Kähler metrics, the volume form ωn associated with a Kähler form ω plays a central role. In weighted Kähler geometry, we consider a Kähler manifold X equipped with a Hamiltonian action of a torus T, a

Thibaut Delcroix, Weighted Kähler geometry and semisimple principal fibrations (Lecture IV)

B236-1 IBS, Korea, Republic of

    Speaker Thibaut Delcroix Université de Montpellier In Kähler geometry, especially in the questions of existence of canonical Kähler metrics, the volume form ωn associated with a Kähler form ω plays a central role. In weighted Kähler geometry, we consider a Kähler manifold X equipped with a Hamiltonian action of a torus T, a

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