In this talk, we aim to give a characterization for local K-stability from a non-Archimedean point of view.
Title: A non-Archimedean characterization of local K-stabilityĪbstract: Log Fano cone singularities are generalizations of cones over log Fano varieties, and have a local K-stability theory extending the one for log Fano varieties. March 1: Yueqiao Wu (University of Michigan) This is partially based on joint work with M. If there is time, I'll discuss some analogous results in the setting of formal schemes (where previously even the existence of a MHS was unknown). I will discuss an enrichment of the category of mixed Hodge structures and some results on the existence of natural objects in this category which allow for the possibility of understanding cycles on complex analytic links. On the other hand, mixed hodge theory is often insufficient for the study of cycles/K-theory in the open or singular settings. This is joint work with Brian Lehmann and Sho Tanimoto.įebruary 22: Deepam Patel (Purdue University)Ībstract: An important application of the theory of mixed Hodge structures is in the study of algebraic cycles or K-theory (for example via the Hodge or Bloch-Beilinson conjectures) of smooth projective varieties. This proves the first of Batyrev's heuristics that make up Geometric Manin's Conjecture for Fano fibrations over arbitrary base curves. In the more general setting of a Fano fibration, we show that these curves come from a-covers of X, and we show that the set of such a-covers up to equivalence form a bounded family. In this talk, we provide a geometric classification of the ways that a family of curves can be nonfree. The components of the space of maps that consist entirely of nonfree curves are particularly difficult to understand.
Nonfree curves, on the other hand, can be much more difficult to understand.
They are smooth points of the space of morphisms, and lie on a unique component of the expected dimension.
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Title: Non-free curves and Geometric Manin's ConjectureĪbstract: When studying the space of maps from a smooth curve B to X, the free curves, that is, those whose restricted tangent bundle has vanishing higher cohomology, are particularly nice. We shall see the historical background of this conjecture, followed by the techniques that go into the proof of the quasi-split case in the analogous situation when X is a smooth scheme over a valuation ring of rank one.įebruary 8: Eric Riedl (University of Notre Dame) Recently, this conjecture has seen progress through the work of Fedorov, Panin and Česnavičius. Location: Zoom (Special Time: 11:30 AM EST)Ībstract: A conjecture of Grothendieck and Serre states that a torsor under a reductive group over a Noetherian regular scheme X is Zariski locally trivial if it is generically trivial. The Journal of Algebraic Geometry is sponsored by Tsinghua University and is distributed by the American Mathematical Society for University Press, Inc.January 25: Arnab Kundu (Université Paris-Saclay) Submission information can be found on the journal's Initial Submissions page. Subscription information is available here. Indexing: This journal is indexed in Science Citation Index™-Expanded, ISI Alerting Services, CompuMath Citation Index®, and Current Contents®, Physical, Chemical & Earth Sciences. In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology.
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