# Algebraic Threefolds: With Special Regard to Problems of by Leonard Roth By Leonard Roth

Similar algebraic geometry books

Mathematical Aspects of Geometric Modeling

This monograph examines intimately definite strategies which are priceless for the modeling of curves and surfaces and emphasizes the mathematical conception that underlies those principles. the 2 relevant subject matters of the textual content are using piecewise polynomial illustration (this topic seems in a single shape or one other in each chapter), and iterative refinement, also referred to as subdivision.

Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure

Fractal styles have emerged in lots of contexts, yet what precisely is a trend? How can one make designated the constructions mendacity inside gadgets and the relationships among them? This e-book proposes new notions of coherent geometric constitution to supply a clean method of this generic box. It develops a brand new notion of self-similarity known as "BPI" or "big items of itself," which makes the sector a lot more uncomplicated for individuals to go into.

Singularity Theory I

From the studies of the 1st printing of this booklet, released as quantity 6 of the Encyclopaedia of Mathematical Sciences: ". .. My normal effect is of a very great e-book, with a well-balanced bibliography, prompt! "Medelingen van Het Wiskundig Genootschap, 1995". .. The authors provide the following an up to the moment advisor to the subject and its major purposes, together with a couple of new effects.

Extra info for Algebraic Threefolds: With Special Regard to Problems of Rationality

Sample text

SEVERI has also established the duality law that the base number for varieties ~ is equal to that of varieties Va- k • In the case where Va is either a Grassmannian or a SEGRE variety, the problem has been solved from first principles, independently of the above result. Thus, on a Grassmannian, a base for subvarieties of any given dimension is provided by the SCHUBERT varieties of that dimension (see SEVERI, c; HODGE and PEDOE, a). The various bases for submanifolds on a SEGRE variety have been determined by BENEDICTY .

The adjoint curves of order n - 2 cut on W~ a linear series g~=~, determinable in K, which, if n > 3, can be mapped on the prime sections of a non-singular normal curve V~-2. By repetition of this process, we can transform V~ birationally in K either to a twisted cubic or a conic, according as n is odd or even; and in the former case we can further transform V~ birationally to a line, for the twisted cubic projects into a monoid. Hence, any nonsingular rational curve of order n can be transformed birationally, in K, to a line or a conic, according as n is odd or even (N OETHER [1 J).

E. not reflected in automorphisms of t(x, y, z, ... ). Examples of these phenomena are given in ROTH [I5J, where the corresponding theory for fourfolds is also illustrated. The problem of the base for subvarieties Vk of any dimension k on Va has been solved by SEVERI [7J, using topological methods, subject to the hypothesis that, on ~, arithmetical equivalence of subvarieties implies algebraic equivalence. SEVERI has also established the duality law that the base number for varieties ~ is equal to that of varieties Va- k • In the case where Va is either a Grassmannian or a SEGRE variety, the problem has been solved from first principles, independently of the above result.