![]() This is a joint work with Michele Torielli. Moreover, I will describe the relations between freeness over the rationals and over fields of finite characteristic. Title: On the freeness of hyperplane arrangements over arbitrary fields.Ībstract: In this talk I will recall the basic properties of hyperplane arrangements and their freeness. In this talk we will discuss the question for 3-arrangements. In a recent work by Abe and the speaker, it is shown that the question is not true when the dimension of the vector space is grater than 3. Holm asked whether all arrangements are m-free for m large enough and he proved that the question is true for 2-arrangements. INTERSECTION LATTICE HYPERPLAN FREETitle: High order freeness for 3-arrangementsĪbstract: The m-free arrangement is a generalisation of the free arrangement where m is a nonnegative integer. In applications, I will classify the singularities of affine hypertoric varieties and I will count the number of non-isomorphic crepant resolutions of affine hypertoric varieties in terms of hyperplane arrangements. In this talk, I will discuss (Poisson) deformation of hypertoric varieties. As the geometric properties of (projective) topic varieties can be studied by the associated polytopes, hypertoric varieties can be studied by its associated hyperplane arrangements. Title: Hypertoric varieties and hyperplane arrangementsĪbstract: Hypertoric varieties are algebraic varieties, defined as an analogue of topic varieties. As a corollary, we compute the Falk invariant for the cone of Shi, Linial and semiorder arrangements. In this article, we give a combinatorial formula for this invariant in the case of hyperplane arrangements that are complete lift representation of certain gain graphs. INTERSECTION LATTICE HYPERPLAN SERIESthe third rank of successive quotients in the lower central series of the fundamental group of the arrangement. Title: On the Falk Invariant of Shi-arrangementĪbstract: It is an open question to give a combinatorial interpretation of the Falk invariant of a hyperplane arrangement, i.e. Also, we will discuss the local freeness, Chern and characteristic polynomials and their multiple roots. By this combinatorialization, we can construct new classes of free arrangements called the divisionally and additionally free arrangements in which Terao's conjecture is true. In this talk we show that Terao's addition-deletion theorems are combinatorial, i.e., if you are given one free arrangement among the triple, then whether all of them are free or not depends only on the intersection lattice. Based on them the inductively free arrangements has been constructed in which Terao's conjecture is true. Title: Combinatorics of the addition-deletion theorems for arrangementsĪbstract: The most useful methods to study free arrangements is Terao's addition-deletion theorems. Shuhei Tsujie (Hiroshima Kokusai Gakuin University) Hiroo Tokunaga (Tokyo Metropolitan University) Norihiro Nakashima (Nagoya Institute of Technology) Place: Department of Mathematics, Hokkaido University, Bldg no.4, 4-501 lecture room. 20 (Wednesday) February - 22 (Friday) February 2019 ![]()
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