Towards toric absolute factorization
نویسندگان
چکیده
This article gives an algorithm to recover the absolute factorization of a bivariate polynomial, taking into account the geometry of its monomials. It is based on algebraic criterions inherited from algebraic interpolation and toric geometry.
منابع مشابه
Algebraic Osculation and Factorization of Sparse Polynomials
We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of C and D an effective divisor with support ∂X = X \ C. Our main result gives explicit conditions equivalent to that a given Cartier divisor on the subscheme (|D|,OD) extends to X. These osculation criterions are expressed with residu...
متن کاملOn Oda’s Strong Factorization Conjecture
The Oda’s Strong Factorization Conjecture states that a proper birational map between smooth toric varieties can be decomposed as a sequence of smooth toric blowups followed by a sequence of smooth toric blowdowns. This article describes an algorithm that conjecturally constructs such a decomposition. Several reductions and simplifications of the algorithm are presented and some special cases o...
متن کاملA Note on the Factorization Theorem of Toric Birational Maps after Morelli and Its Toroidal Extension
Building upon the work of [Morelli1,2], we give a coherent presentation of Morelli’s algorithm for the weak and strong factorization of toric birational maps. We also discuss its toroidal extension, which plays a crucial role in the recent solutions [W lodarczyk2,3, Abramovich-Karu-Matsuki-W lodarczyk] of the weak factorization conjecture of general birational maps.
متن کاملImplicitizing Bi-Cubic Toric Surfaces by Dixon? - Resultant Quotients
Toric surface patches have two significant geometric properties: they are multi-sided and they are generalizations of both the triangular and rectangular Bezier surface patches. They also have a very nice algebraic property: their implicit equations are closely related to the Dixon determinant. In particular, for bi-cubic toric patches without base points, their implicit equation can always be ...
متن کاملLocal Strong Factorization of Birational Maps
The strong factorization conjecture states that a proper birational map between smooth algebraic varieties over a field of characteristic zero can be factored as a sequence of smooth blowups followed by a sequence of smooth blowdowns. We prove a local version of the strong factorization conjecture for toric varieties. Combining this result with the monomialization theorem of S. D. Cutkosky, we ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 44 شماره
صفحات -
تاریخ انتشار 2009