In this talk I will discuss the proof of the Lefschetz standard conjectures in certain degrees for varieties of generalized Kummer deformation type.
In modern algebraic geometry, they are essential for the theory of motives, and imply the variational Hodge conjecture, among other things. The conjectures imply that the Kunneth components of the diagonal of X × X are algebraic and that homological and numerical equivalence coincide. The Lefschetz standard conjectures for generalized kummer varieties.įor a projective variety X/k, the Lefschetz standard conjectures of Grothendieck posit the existence of certain algebraic cycles in X × X. In this talk, I'll work in the more general setting of automorphism groups of quasismooth hypersurfaces in weighted projective space and consider the following questions: when are these groups linear? When are they finite, and if finite, how large can they get? What does the automorphism group of a very general hypersurface with given weights and degree look like? In each case, I'll consider generalizations of the analogous results for ordinary projective hypersurfaces and explain how unexpected behavior appears in the weighted setting. This will involve a careful study of the boundary strata of the moduli space.Īutomorphisms of Weighted Projective Hypersurfaces.Īutomorphism groups of smooth hypersurfaces in projective space are well studied in algebraic geometry. To achieve this, we will identify the desired homology class and provide an explicit description of a closed embedding from T d,n to the Chow variety. In this talk, we will demonstrate how the moduli space T d,n discussed previously in this seminar is isomorphic, up to normalization, to a closed subset of an appropriately chosen Chow variety. More specifically, it parametrizes subvarieties with the same homology class in the standard topology. The Chow variety is a compact space that parametrizes closed subvarieties of projective space (or products thereof) with the same dimension and degree. The moduli space T d,n as a Chow quotient. Location: Online via Zoom (Please email the organizers if interested.) We usually meet in Skye 268, but the meetings are online via Zoom during Spring 2023.įor more information you may contact Ziv Ran Jose Gonzalez or Patricio Gallardo find our schedule below.įor information about reimbursements for our visitors click here. If you drive, the most convenient public parking is in the pay lot whose entrance is on 34th Street between Market and Chestnut Streets.The UC Riverside Algebraic Geometry Seminar meets on Tuesdays from 11:00am to 12:00pm. Coming from the airport by train (about 15 minutes): the University City Rail Station is the second stop after you leave the airport. We are about a 15 minute walk from the main 30th Street Station and 5 minutes from the University City Rail Station at 32nd and Spruce (=South Street & Convention Avenue). Note 33rd Street runs one way north while Walnut runs one way west. The building is at 209 South 33rd Street (the Southeast corner of 33rd. The Mathematics Department Office is located on the fourth (top) floor of David Rittenhouse Laboratory ("DRL").
#PRINCETON ALGEBRAIC GEOMETRY SEMINAR HOW TO#
How to get to Penn's Mathematics Department
0 kommentar(er)
