Neron-severi Group for Torus Quasi Bundles over Curves
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Effective Divisor Classes on a Ruled Surface
The Neron-Severi group of divisor classes modulo algebraic equivalence on a smooth algebraic surface is often not difficult to calculate, and has classically been studied as one of the fundamental invariants of the surface. A more difficult problem is the determination of those divisor classes which can be represented by effective divisors; these divisor classes form a monoid contained in the N...
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Let X be an irreducible smooth geometrically integral projective surface over a field. In this paper we give an effective bound in terms of the Neron–Severi rank ρ(X) of X for the number of irreducible curves C on X with negative self-intersection and geometric genus less than b1(X)/4, where b1(X) is the first étale Betti number of X. The proof involves a hyperbolic analog of the theory of sphe...
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In this paper we construct some algebraic geometric error-correcting codes on surfaces whose Neron-Severi group has low rank. If the rank of the Neron-Severi group is 1, the intersection of this surface with an irreducible surface of lower degree will be an irreducible curve, and this makes possible the construction of codes with good parameters. Rank 1 surfaces are not easy to find, but we are...
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The existence problem for vector bundles on a smooth compact complex surface consists in determining which topological complex vector bundles admit holomorphic structures. For projective surfaces, Schwarzenberger proved that a topological complex vector bundle admits a holomorphic (algebraic) structure if and only if its first Chern class belongs to the Neron-Severi group of the surface. In con...
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The existence problem for vector bundles on a smooth compact complex surface consists in determining which topological complex vector bundles admit holomorphic structures. For projective surfaces, Schwarzenberger proved that a topological complex vector bundle admits a holomorphic (algebraic) structure if and only if its first Chern class belongs to the Neron-Severi group of the surface. In con...
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