Let X be a projective manifold and f : X → X a rational mapping with large topological degree, dt λk−1 (f ) := the (k − 1)th dynamical degree of f . We give an elementary construction of a probability measure µf such that d−n (f n )∗ Θ → µf for every smooth probability measure Θ on X. We show t that every quasiplurisubharmonic function is µf -integrable. In particular µf does not charge either points of indeterminacy or pluripolar sets, hence µf is f -invariant with constant jacobian f ∗ µf = dt µf...
Most enterprises deal with a single end product, which indicates the high degree of specialisation
of the enterprises in Jepara. The vast majority (95.5%) are enterprises run by a single extended
family, while relatively few involved two (4.3%) or three (0.2%) separate families or lineages. Almost
all enterprises had at least one other regular partner enterprise, even if there were no links in
the ownership of the enterprises.
Israel Moiseevich Gelfand is one of the greatest mathematicians of the 20th century.
His insights and ideas have helped to develop new areas in mathematics and to
reshape many classical ones.
The influence of Gelfand can be found everywhere in mathematics and mathematical
physics from functional analysis to geometry, algebra, and number theory. His
seminar (one of the most influential in the history of mathematics) helped to create
a very diverse and productive Gelfand school; indeed, many outstanding mathematicians
proudly call themselves Gelfand disciples....
The interplay between geometry and topology on complex algebraic varieties is a classical theme that goes back to Lefschetz [L] and Zariski [Z] and is always present on the scene; see for instance the work by Libgober [Li]. In this paper we study complements of hypersurfaces, with special attention to the case of hyperplane arrangements as discussed in Orlik-Terao’s book [OT1]. Theorem 1 expresses the degree of the gradient map associated to any homogeneous polynomial h as the number of n-cells that have to be added to a generic hyperplane section D(h) ∩ H to obtain the complement in...