Toric degenerations of Schubert varieties

Families of toric varieties

✍ Mihai Halic 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 351 KB

## Abstract The goal of this article is to construct families of complete toric varieties over arbitrary bases, and to compute the cohomology of the total space. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Quotients of toric varieties

✍ M. M. Kapranov; B. Sturmfels; A. V. Zelevinsky 📂 Article 📅 1991 🏛 Springer 🌐 English ⚖ 877 KB

Syzygies of affine toric varieties

✍ Antonio Campillo; Philippe Gimenez 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 996 KB

We give a method for computing the syzygies of the coordinate ring R of an affine toric variety. We show how the method works for dimension one and two cases, Cohen-Macaulay semigroups, and for computing minimal generators of the defining ideal. We show how to compute the depth of R and generalize a

Intersections of Schubert Varieties

✍ S.B. Mulay 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 214 KB

Let k be a field and let FL n, k denote the variety of full flags on an n-dimensional vector space over k. This variety can also be identified with Ž . the quotient GrB where G s GL n, k , and B is the subgroup consisting Ž w x. of all upper-triangular matrices. It is well known that e.g., see 7 Ž .

Toric Degenerations of Polynomial Ideals

Toric Degenerations of Polynomial Ideals and Geometric Localization of Fans

✍ STÉPHANE COLLART; DANIEL MALL 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 580 KB

Toric degenerations of polynomial ideals occur if one allows certain partial term orders in the theory of Gröbner bases. We prove that the collection of toric degenerations of an ideal can be monotonically embedded into the complex closure of the Gröbner fan. A process of geometric localization on t

The Regularity of a Toric Variety

✍ E Briales-Morales; P Pisón-Casares; A Vigneron-Tenorio 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 164 KB

We give a method for computing the degrees of the minimal syzygies of a toric variety by means of combinatorial techniques. Indeed, we complete the explicit description of the minimal free resolution of the associated semigroup algebra, using the simplicial representation of Koszul homology which ap