Humboldt-Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik
Wintersemester 2025-2026
Time: Wednesday 13:15 - 14:45
Room: 3.007 John von Neumann-Haus
Humboldt Arithmetic Geometry Seminar
Seminar: Algebraic Geometry an der FU
| Time | Speaker | |
|---|---|---|
| 22.10.2025, 13:15 - 14: 45 | Jinhyung Park (KAIST Daejeon) | |
| Title: Determinantal ideals of secant varieties | ||
| Abstract: We show that the homogeneous ideals of secant varieties of smooth projective curves and surfaces in sufficiently ample embeddings are determinantally presented. The same result holds for the first secant varieties of arbitrary smooth projective varieties in sufficiently ample embeddings. This completely settles a conjecture of Eisenbud-Koh-Stillman for curves and partially resolves a conjecture of Sidman-Smith in higher dimensions. To establish the results, we employ the geometry of Hilbert schemes of points. Based on our method, we also prove that the homogeneous ideals of arbitrary projective schemes in sufficiently ample embeddings are generated by quadrics of rank three, confirming a conjecture of Han-Lee-Moon-Park. This is joint work with Daniele Agostini. | ||
| 29.10.2025, 13:15 - 14:45 | Pawel Borowka (Jagiellonian University) | |
| Title: Some questions about abelian surfaces | ||
| Abstract: At the end of 19th century, Humbert characterised the locus of principally polarised abelian surfaces that contain elliptic curves. This locus has infinitely many irreducible components, called Humbert surfaces. The components can be indexed by natural numbers that are exponents of complementary elliptic curves. We would like to describe irreducible components for non-principally polarised abelian surfaces. In the talk, after a brief overview of principally polarised case, I will show some results based on a joint paper with R. Auffarth. I will restate some questions posed in the article and if time permits I will talk about a possible way to answer them. | ||
| 5.11.2025, 13:15 - 14:45 | Daebeom Choi (University of Pennsylvania) | |
| Title: Extremal effective curves and non-semiample line bundles on the moduli space of curves. | ||
| Abstract: In this work, we develop a new method for establishing extremality in the closed cone of curves on the moduli space of curves and determine the extremality of many boundary 1-strata. As a consequence, by using a general criterion for non-semiampleness that extends Keel's argument, we demonstrate that a substantial portion of the cone of nef divisors on the moduli space of pointed curves is not semiample. As an application, we construct the first explicit example of a non-contractible extremal ray of the closed cone of effective curves on the moduli space of n-pointed curves of genus 3. Moreover, we show that this extremal ray is contractible in characteristic p. Our method relies on two main ingredients: (1) the construction of a new collection of nef divisors, and (2) the identification of a tractable inductive structure on the Picard group, arising from Knudsen's construction of the moduli space. | ||
| 10.11.2025, 13:15 - 14:45 | Rahul Pandharipande (ETH Zürich) | |
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| 12.11.2025, 13:15 - 14:45 | Nathan Pflueger (Amherst College) | |
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| 26.11.2025, 13:15 - 14:45 | Margherita Lelli-Chiesa (Universita Roma Tre) | |
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