Jumping deformations of complete toric varieties
نویسندگان
چکیده
We construct one-parameter complex analytic families whose special fibers are complete toric varieties. Under some assumptions, the general fibers of these families also become toric varieties and we can explicitly describe the corresponding fans from the data of the fans corresponding to the special fibers. Using these families, we give a deformation family for a certain toric weakened Fano 3-fold. Moreover, we get some examples of toric weakened Fano 4-folds.
منابع مشابه
Log geometry and multiplier ideals
I work in combinatorics, algebraic geometry, convex geometry and commutative algebra while staying informed on certain topics in category theory and ring theory. In particular, I focus on toric varieties and singularity theory. The study of toric varieties lies at the intersection of combinatorics, algebraic geometry, convex geometry and integer programming. There is a correspondence between ce...
متن کاملDeformations of Codimension 2 Toric Varieties
We prove Sturmfels’ conjecture that toric varieties of codimension two have no other flat deformations than those obtained by Gröbner basis theory.
متن کاملMutations of Laurent Polynomials and Flat Families with Toric Fibers
We give a general criterion for two toric varieties to appear as fibers in a flat family over P. We apply this to show that certain birational transformations mapping a Laurent polynomial to another Laurent polynomial correspond to deformations between the associated toric varieties.
متن کاملToric Fano varieties with divisorial contractions to curves
In this paper, we obtain a complete classification of smooth toric Fano varieties equipped with extremal contractions which contract divisors to curves for any dimension. As an application, we obtain a complete classification of smooth projective toric varieties which can be equivariantly blown-up to Fano along curves.
متن کاملLarge Complex Structure Limits, Quantization and Compact Tropical Amoebas on Toric Varieties
We consider toric deformations of complex structures, described by the symplectic potentials of Abreu and Guillemin, with degenerate limits of the holomorphic polarization corresponding to the toric Lagrangian fibration, in the sense of geometric quantization. This allows us to interpolate continuously between quantizations in the holomorphic and real polarizations and show that the monomial ho...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002