Designing tools for Analytic Geometry: the Quadrics
نویسندگان
چکیده
منابع مشابه
Birational geometry of quadrics
A central method in the theory of quadratic forms is the study of function fields of projective quadrics. In particular, it is important to ask when there is a rational map from one quadric over a field to another. This suggests the problem of determining when two quadrics are birational, which turns out to be much harder. The answer is known for quadratic forms of dimension at most 7 (thus for...
متن کاملOn the Geometry of Generalised Quadrics
Let {f0, · · · , fn; g0, · · · , gn} be a sequence of homogeneous polynomials in 2n + 2 variables with no common zeroes in P and suppose that the degrees of the polynomials are such that Q = ∑n i=0 figi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalised quadric. In this note, we prove that generalised quadrics in P C for n ≥ 1 are reduced.
متن کاملOn the Geometry of Generalized Quadrics
Let {f0, · · · , fn; g0, · · · , gn} be a sequence of homogeneous polynomials in 2n + 2 variables with no common zeroes in P and suppose that the degrees of the polynomials are such that Q = ∑n i=0 figi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalized quadric. In this note, we prove that generalized quadrics in P C for n ≥ 1 are reduced.
متن کاملBirational geometry of quadrics in characteristic 2
The theory of quadratic forms can be regarded as studying an important special case of the general problem of birational classification of algebraic varieties. A typical example of a Fano fibration in minimal model theory is a quadric bundle, which can be viewed without loss of information as a quadric hypersurface over the function field of the base variety. This description feeds the problem ...
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main purpose of the present research is to invent some tools for confirming hypotheses in analytic-reasoning researches. for this regard, the analytic research is used. the present tools, weighting to reasons tool (wrt) and repeat reasoning tool (rrt) are used for evaluating hypotheses of the current research. the results of the wrt shows that reasons weight (rw) for the first hypothesis is 8 a...
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ژورنال
عنوان ژورنال: New Trends and Issues Proceedings on Humanities and Social Sciences
سال: 2017
ISSN: 2547-8818
DOI: 10.18844/prosoc.v4i3.2643