Bài giảng viện

Laplace Equations and the Weak Lefschetz Property
Người báo cáo: Giáo sư Rosa M. Míró – Roig, University of Barcelona, Spain

Thời gian: 9h30-10h30, thứ 6, ngày 7//3/2014

Địa điểm: Phòng 301, Nhà A5, Viện Toán học, 18 Hoàng Quốc Việt Cầu Giấy, Hà Nội

Tóm tắt: The goal of my talk is to establish a close relationship between a priori two unrelated problems:

  1. Algebraic Problem: the existence of homogeneous artinian ideals $Isubset k[x_0, cdots, x_n]$ which fail the Weak Lefschetz Property; and
  2. Classical Geometric Problem: the existence of (smooth) projective varieties $X subset PP^N$ satisfying at least one Laplace equation of order $s geq 2$. These are two longstanding problems which  lie at the crossroads between Commutative Algebra, Algebraic Geometry, Differential Geometry and Combinatorics.

In the toric case, I will classify some relevant examples  and as byproduct  I will provide counterexamples to Ilardi's conjecture.

Finally, I will classify all smooth Togliatti system of cubics and solve a conjecture stated in my joint work with Mezzetti and Ottaviani.
All I will say is based in joint work with either  E. Mezzetti and G. Ottaviani or M. Michalek.

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