2,016 research outputs found
The cone of pseudo-effective divisors of log varieties after Batyrev
In these notes we investigate the cone of nef curves of projective varieties,
which is the dual cone to the cone of pseudo-effective divisors. We prove a
structure theorem for the cone of nef curves of projective -factorial klt pairs of arbitrary dimension from the point of view of the
Minimal Model Program. This is a generalization of Batyrev's structure theorem
for the cone of nef curves of projective terminal threefolds.Comment: 15 pages. v2: Completely rewritten paper. Structure theorem for the
cone of nef curves proved in arbitrary dimension using results of Birkar,
Cascini, Hacon and McKernan. To appear in Mathematische Zeitschrif
Analysis of the effectiveness of industrial R and D
The criteria used by private industry in evaluating and selecting proposed research and development projects for implementation, and also in determining which R and D facilities are to be acquired were investigated. Conceptual and practical issues inherent in any quantitative analysis of the contribution of R and D to economic growth were identified in order to assist NASA in developing approaches for analzying the economic implication of its own R and D efforts
Inclusion-exclusion and Segre classes
We propose a variation of the notion of Segre class, by forcing a naive
`inclusion-exclusion' principle to hold. The resulting class is computationally
tractable, and is closely related to Chern-Schwartz-MacPherson classes. We
deduce several general properties of the new class from this relation, and
obtain an expression for the Milnor class of a scheme in terms of this class.Comment: 8 page
Noncommutative ampleness for multiple divisors
The twisted homogeneous coordinate ring is one of the basic constructions of
the noncommutative projective geometry of Artin, Van den Bergh, and others.
Chan generalized this construction to the multi-homogeneous case, using a
concept of right ampleness for a finite collection of invertible sheaves and
automorphisms of a projective scheme. From this he derives that certain
multi-homogeneous rings, such as tensor products of twisted homogeneous
coordinate rings, are right noetherian. We show that right and left ampleness
are equivalent and that there is a simple criterion for such ampleness. Thus we
find under natural hypotheses that multi-homogeneous coordinate rings are
noetherian and have integer GK-dimension.Comment: 11 pages, LaTeX, minor corrections, to appear in J. Algebr
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