Zariski surfaces, class groups and linearized systems
نویسندگان
چکیده
منابع مشابه
Completeness in Zariski Groups
Zariski groups are @0-stable groups with an axiomatically given Zariski topology and thus abstract generalizations of algebraic groups. A large part of algebraic geometry can be developed for Zariski groups. As a main result, any simple smooth Zariski group interprets an algebraically closed eld, hence is almost an algebraic group over an algebraically closed eld.
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Remark 1. We quickly recall a couple of definitions Let DivQ(X) := Div(X)⊗Q. On smooth projective surfaces all Q-Weil divisors are also Q-Cartier, hence we can write Q-Cartier every divisor D as a finite sum ∑ xiCi, where the Ci are distinct integral curves and xi ∈ Q. A divisor D is called effective (or sometimes positive) if xi ≥ 0 ∀i. If D · C ≥ 0 for all integral curves C then D we be calle...
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Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Broué-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is invariant-theoretic and does not use the cla...
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For n > 2, let Γn denote either SL(n,Z) or Sp(n,Z). We give a practical algorithm to compute the level of the maximal principal congruence subgroup in an arithmetic group H ≤ Γn. This forms the main component of our methods for computing with such arithmetic groups H. More generally, we provide algorithms for computing with Zariski dense groups in Γn. We use our GAP implementation of the algori...
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The purpose of this note is to obtain a restriction on the fundamental groups of nonelliptic compact complex surfaces of class VII in Kodaira’s classification [9]. We recall that these are the compact complex surfaces with first Betti number one and no nonconstant meromorphic functions. This seems to be the class of compact complex surfaces whose structure is least understood. The first and sim...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2011
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2011.03.011