August 1
(Monday) ～ August 5 (Friday), 2016
ABSTRACT
| August, 1 (Mon) | August, 2 (Tue) | August, 3 (Wed) | August, 4 (Thu) | August, 5 (Fri) |
| 9:30--10:30 | Emanuela De Negri （Genova University）
"Universal Gröbner bases and Cartwright-Sturmfels ideals" |
| By a well-known result of Bernstein-Sturmfels-Zelevinsky,
the maximal minors of a matrix of variables form a universal Gröbner basis.
Also for the ideal of $2$-minors of the matrix of variables the universal Gröbner basis is well described by results of Sturmfels and Villareal. In this talk we generalize these facts; we consider multigraded matrices of linear forms, and find universal Gröbner bases of the ideals of maximal minors and the ideals of $2$-minors. To this aim we introduce two families of multigraded ideals, which we call Cartwright-Sturmfels and Cartwright-Sturmfels$^*$. Both families are characterized by properties of their multigraded generic initial ideals. It turns out that Cartwright-Sturmfels ideals are radical, and that every minimal system of generators of a Cartwright-Sturmfels$^*$ ideal is a universal Gröbner basis. Moreover the two classes are closed under standard operations on ideals, and this allows us to prove the desired results. This is a joint work with Aldo Conca and Elisa Gorla |
|
| 10:45--11:45 | Sijong Kwak （KAIST）
"Characterization of ACM varieties with d-linear resolution" |
| In my talk, I consider the algebraic set, not necessary irreducible, whose graded Bettti table looks to be of the special shape, i.e. property $N_{d,e}$ or property ND(d-1). We can give sharp upper bounds on the graded Betti numbers and degree bound for those categories. Only ACM varieties with d-linear resolution can appear as?the boundary cases for those upper bounds. We explain basic definitions, generic initial ideal theory and projection methods for our characterization. These are the generalization of 2-linear ACM varieties in clasical algebraic geometry. |