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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Hodge Theory
- Proceedings, U.S.-Spain Workshop Held in Sant Cugat (Barcelona), Spain, June 24-30, 1985
(English, French, Paperback, 1987 ed.)
Eduardo H. C. Cattani, Francisco Guillen, Aroldo Kaplan, Fernando Puerta
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R1,203
Discovery Miles 12 030
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Over the past 2O years classical Hodge theory has undergone several
generalizations of great interest in algebraic geometry. The papers
in this volume reflect the recent developments in the areas of:
mixed Hodge theory on the cohomology of singular and open
varieties, on the rational homotopy of algebraic varieties, on the
cohomology of a link, and on the vanishing cycles; L -realization
of the intersection cohomology for the cases of singular varieties
and smooth varieties with degenerating coefficients; applications
of cubical hyperresolutions and of iterated integrals; asymptotic
behavior of degenerating variations of Hodge structure; the
geometric realization of maximal variations; and variations of
mixed Hodge structure. N
The last book XIII of Euclid's Elements deals with the regular
solids which therefore are sometimes considered as crown of
classical geometry. More than two thousand years later around 1850
Schl fli extended the classification of regular solids to four and
more dimensions. A few decades later, thanks to the invention of
group and invariant theory the old three dimensional regular solid
were involved in the development of new mathematical ideas: F.
Klein (Lectures on the Icosa hedron and the Resolution of Equations
of Degree Five, 1884) emphasized the relation of the regular solids
to the finite rotation groups. He introduced complex coordinates
and by means of invariant theory associated polynomial equations
with these groups. These equations in turn describe isolated
singularities of complex surfaces. The structure of the
singularities is investigated by methods of commutative algebra,
algebraic and complex analytic geometry, differential and algebraic
topology. A paper by DuVal from 1934 (see the References), in which
resolutions play an important rele, marked an early stage of these
investigations. Around 1970 Klein's polynomials were again related
to new mathematical ideas: V. I. Arnold established a hierarchy of
critical points of functions in several variables according to
growing com plexity. In this hierarchy Kleinls polynomials describe
the "simple" critical points."
Let G be the group of rational points of a split connected
reductive group over a nonarchimedean local field of residue
characteristic p.LetI be a pro-p Iwahori subgroup of G and let R be
a commutative quasi-Frobenius ring. If H = R[I\G/I] denotes the
pro-p Iwahori- Hecke algebra of G over R we clarify the relation
between the category of H-modules and the category of G-equivariant
coefficient systems on the semisimple Bruhat-Tits building of G.IfR
is a field of characteristic zero this yields alternative proofs of
the exactness of the Schneider-Stuhler resolution and of the
Zelevinski conjecture for smooth G-representations generated by
their I-invariants. In general, it gives a description of the
derived category of H-modules in terms of smooth G-representations
and yields a functor to generalized (?, ?)-modules extending the
constructions of Colmez, Schneider and Vigneras.
A characterization is given for the factorizations of almost simple
groups with a solvable factor. It turns out that there are only
several infinite families of these non-trivial factorizations, and
an almost simple group with such a factorization cannot have socle
exceptional Lie type or orthogonal of minus type. The
characterization is then applied to study s-arc-transitive Cayley
graphs of solvable groups, leading to a striking corollary that,
except for cycles, a non-bipartite connected 3-arc-transitive
Cayley graph of a finite solvable group is necessarily a normal
cover of the Petersen graph or the Ho?man-Singleton graph.
The Galois theory of di?erence equations has witnessed a major
evolution in the last two decades. In the particular case of
q-di?erence equations, authors have introduced several di?erent
Galois theories. In this memoir we consider an arithmetic approach
to the Galois theory of q-di?erence equations and we use it to
establish an arithmetical description of some of the Galois groups
attached to q-di?erence systems.
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Geometrie Algebrique Reelle et Formes Quadratiques
- Journees S.M.F., Universite De Rennes 1, Mai 1981
(English, German, French, Paperback, 1982 ed.)
Jean-Louis Colliot-Thelene, Michel Coste, Louis Mah e, Marie-Francoise Roy
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R1,870
Discovery Miles 18 700
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