Computation of Unirational Fields
نویسندگان
چکیده
One of the main contributions which Volker Weispfenning made to mathematics is related to Gröbner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational field extension (which in particular includes the zero characteristic case). One of the main tools is Gröbner bases theory. Our algorithm also requires computing primitive elements and factoring over algebraic extensions. Moreover, the method can be extended to finitely generated K-algebras.
منابع مشابه
Computation of unirational fields (extended abstract)
In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational field extension (which in particular includes the zero characteristic case). One of the main tools is Gröbner bases theory, see [BW93]. Our algorithm also requires computing computing primitive elements and factoring over algebraic extensions. Moreover, the method can be...
متن کاملUnirationality and Existence of Infinitely Transitive Models
We study unirational algebraic varieties and the fields of rational functions on them. We show that after adding a finite number of variables some of these fields admit an infinitely transitive model. The latter is an algebraic variety with the given field of rational functions and an infinitely transitive regular action of an algebraic group generated by unipotent algebraic subgroups. We expec...
متن کاملDegree of Unirationality for Del Pezzo Surfaces over Finite Fields
We address the question of the degree of unirational parameterizations of degree four and degree three del Pezzo surfaces. Specifically we show that degree four del Pezzo surfaces over finite fields admit degree two parameterizations and minimal cubic surfaces admit parameterizations of degree 6. It is an open question whether or not minimal cubic surfaces over finite fields can admit degree 3 ...
متن کاملEfficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields
This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...
متن کاملUnirationality of Cubic Hypersurfaces
A remarkable result of [Segre43] says that a smooth cubic surface over Q is unirational iff it has a rational point. [Manin72, II.2] observed that similar arguments work for higher dimensional cubic hypersurfaces satisfying a certain genericity assumption over any infinite field. [CT-S-SD87, 2.3.1] extended the result of Segre to any normal cubic hypersurface (other than cones) over a field of ...
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 41 شماره
صفحات -
تاریخ انتشار 2005