5,802 research outputs found
Cuspidal curves, minimal models and Zaidenberg's finiteness conjecture
Let be a complex rational cuspidal curve and let
be the minimal log resolution of singularities. We
prove that has at most six cusps and we establish an effective version
of the Zaidenberg Finiteness Conjecture (1994) concerning Eisenbud-Neumann
diagrams of . This is done by analysing the Minimal Model Program run for
the pair . Namely, we show that is
-fibred or for the log resolution of the minimal model the
Picard rank, the number of boundary components and their self-intersections are
bounded.Comment: 24 page
A new proof of the theorems of Lin-Zaidenberg and Abhyankar-Moh-Suzuki
Using the theory of minimal models of quasi-projective surfaces we give a new
proof of the theorem of Lin-Zaidenberg which says that every topologically
contractible algebraic curve in the complex affine plane has equation
in some algebraic coordinates on the plane. This gives also a proof of the
theorem of Abhyankar-Moh-Suzuki concerning embeddings of the complex line into
the plane. Independently, we show how to deduce the latter theorem from basic
properties of -acyclic surfaces.Comment: 12 pages, 1 figur
The Coolidge-Nagata conjecture, part I
Let be a complex rational cuspidal curve contained
in the projective plane and let be the minimal log
resolution of singularities. Applying the log minimal model program to
we prove that if has more than two singular points or if
, which is a tree of rational curves, has more than six maximal twigs or if
is not of log general type then is Cremona
equivalent to a line, i.e. the Coolidge-Nagata conjecture for holds. We
show also that if is not Cremona equivalent to a line then the morphism
onto the minimal model contracts at most one irreducible curve not contained in
.Comment: 34 pages, 1 figur
The Coolidge-Nagata conjecture holds for curves with more than four cusps
Let E be a plane rational curve defined over complex numbers which has only
locally irreducible singularities. The Coolidge-Nagata conjecture states that E
is rectifiable, i.e. it can be transformed into a line by a birational
automorphism of the plane. We show that if it is not rectifiable then the tree
of the exceptional divisor for its minimal embedded resolution of singularities
has at most nine maximal twigs. This settles the conjecture in case E has more
than four singular points.Comment: 11 page
Classification of planar rational cuspidal curves. II. Log del Pezzo models
Let be a complex curve homeomorphic to the
projective line. The Negativity Conjecture asserts that the Kodaira-Iitaka
dimension of , where is a
minimal log resolution, is negative. We prove structure theorems for curves
satisfying this conjecture and we finish their classification up to a
projective equivalence by describing the ones whose complement admits no
-fibration. As a consequence, we show that they satisfy the
Strong Rigidity Conjecture of Flenner-Zaidenberg. The proofs are based on the
almost minimal model program. The obtained list contains one new series of
bicuspidal curves.Comment: 50 page
IMPACT OF AMT INVESTMENTS ON EFFECTIVENESS AND COMPETITIVENESS OF MANUFACTURING SYSTEMS
Every manufacturing company is a system of individual manufacturing units, which have to be carefully laid out taking into account time, space, technology, and organisation perspective in order to deliver maximum final product. In order to secure absolute effective and efficient functionality of manufacturing process all manufacturing units have to be reviewed already in stage of its planning and organising. Only continual process of measuring, evaluating and managing effectiveness of individual manufacturing units as well as whole manufacturing system will provide sustainable competitive advantage. The goal of the article is therefore propose methods of evaluation of effectiveness of Advanced Manufacturing Technology(AMT).Effectiveness, Layout, Manufacturing System, Evaluation.
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