Rational surfaces in P4 containing a plane curveThe families of smooth rational surfaces in 4 have been classified in degree 10. All known rational surfaces in 4 can be represented as blow-ups of the plane 2. The fine…Fabrizio Catanese, Klaus Hulek·May 23, 1995SaveLearn
Lang's conjectures, Conjecture H, and uniformityThe purpose of this note is to wish a happy birthday to Professor Lucia Caporaso.* We prove that Conjecture H of Caporaso et. al. ([CHarM], sec. 6) together with Lang's conjecture implies the…Dan Abramovich·May 21, 1995SaveLearn
Mapping threefolds onto three-quadricsWe prove that the degree of a nonconstant morphism from a smooth projective 3-fold X with Néron-Severi group Z to a smooth 3-dimensional quadric is bounded in terms of numerical invariants…Carmen Schuhmann·May 19, 1995SaveLearn
Rational Blowdowns of Smooth 4-ManifoldsIn this paper we introduce a surgical procedure, called a rational blowdown, for a smooth 4-manifold X and determine how this procedure affects both the Donaldson and Seiberg-Witten invariants of X.Ronald Fintushel, Ronald Stern·May 17, 1995SaveLearn
On projective plane curves whose complements have finite non-abelian fundamental groupsWe construct new examples of singular projective plane curves whose complements have finite and non-abelian fundamental groups, by generalizing the classical three cuspidal quartic curve discovered…Ichiro Shimada·May 15, 1995SaveLearn
Iitaka-Severi's Conjecture for Complex ThreefoldsWe prove the following generalization of Severi's Theorem: Let X be a fixed complex variety. Then there exist, up to birational equivalence, only finitely many complex varieties Y of general…Gerd Dethloff·May 12, 1995SaveLearn
Stratified Picard--Lefschetz theoryThe monodromy action in the homology of level sets of Morse functions on stratified singular analytic varieties is studied. The local variation operators in both the standard and the intersection…Victor Vassiliev·May 11, 1995SaveLearn
Seiberg-Witten Invariants and Rationality of Complex SurfacesThe purpose of this paper is: 1) to explain the Seiberg-Witten invariants, 2) to show that - on a Kähler surface - the solutions of the monopole equations can be interpreted as algebraic objects,…Andrei Teleman, Christian Okonek·May 8, 1995SaveLearn
Seiberg-Witten Invariants and the Van De Ven ConjectureThe purpose of this note is to give a short, selfcontained proof of the following result: A complex surface which is diffeomeorphic to a rational surface is rational.Andrei Teleman, Christian Okonek·May 8, 1995SaveLearn
The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairsWe introduce coupled Seiberg-Witten equations, and we prove, using a generalized vortex equation, that, for Kaehler surfaces, the moduli space of solutions of these equations can be identified with a…Ch. Okonek, A. Teleman·May 8, 1995SaveLearn
Les Invariants de Seiberg-Witten et la Conjecture de Van De VenWe give a short proof for the fact that rationality of complex surfaces is a property depending only on the differential structure. Our proof uses the new Seiberg-Witten invariants.Ch. Okonek, A. Teleman·May 8, 1995SaveLearn
Algebraic Barth-Lefschetz theoremsUsing results of Hironaka-Matsumura and Faltings, we prove a strong version of the well known Fulton-Hansen connectivity theorem for weighted projective spaces. As a consequence we get the following…Lucian Badescu·May 8, 1995SaveLearn
Spectral CoversThis is a survey of various results about spectral covers and their relationship to Higgs bundles. To a G-principal Higgs bundle on a variety S corresponds a cameral cover S of S (a…Ron Donagi·May 7, 1995SaveLearn
Un critère d'extension d'un foncteur défini sur les schémas lissesLet k be a field of characteristic zero. By using Hironaka's desingularisation theorem, we prove an extension criterion for a functor defined on nonsingular k-schemes and taking values on a…F. Guillén, V. Navarro Aznar·May 5, 1995SaveLearn
A note on Zariski pairsA couple of complex projective plane curves are said to make a Zariski pair if they have the same degree and the same type of singularities, but their embeddings in the projective plane are…Ichiro Shimada·May 5, 1995SaveLearn
Blowups and gauge fieldsThe relationship between stable holomorphic vector bundles on a compact complex surface and the same such objects on a blowup of the surface is investigated, where "stability" is with respect…Nicholas P. Buchdahl·May 5, 1995SaveLearn
Sequences of stable bundles over a compact complex surfaceWhen identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact complex surface…Nicholas P. Buchdahl·May 5, 1995SaveLearn
Bogomolov conjecture over function fields for stable curves with only irreducible fibers (Version 2.0)Let K be a function field and C a non-isotrivial curve of genus g >= 2 over K. In this paper, we will show that if C has a global stable model with only geometrically irreducible fibers, then…Atsushi Moriwaki·May 4, 1995SaveLearn
A weighted version of Zariski's hyperplane section theorem and fundamental groups of complements of plane curvesWe formulate and prove a weighted version of Zariski's hyperplane section theorem on the topological fundamental groups of the complements of hypersurfaces in a projective space. As an…Ichiro Shimada·May 4, 1995SaveLearn
Quantum cohomology of flag varietiesWe describe a construction of Gromov-Witten invariants for flag varieties and use it to give a presentation for the quantum cohomology ring, by extending the ideas used by Bertram in the case of…Ionuţ Ciocan-Fontanine·May 3, 1995SaveLearn
Pieri's rule for flag manifolds and Schubert polynomialsWe establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a…Frank Sottile·May 2, 1995SaveLearn
A Non-Linear Deformation of the Hitchin Dynamical SystemMukai's space, parametrizing simple sheaves on a K3 surface S whose numerical invariants are those of a line bundle on a curve C in S, is interpreted as a deformation of Hitchin's system on…Ron Donagi, Lawrence Ein, Robert Lazarsfeld·Apr 30, 1995SaveLearn
Gauge fixing for logarithmic connections over curves and the Riemann-Hilbert-ProblemWe explain in detail the correspondence between algebraic connections over CP1, logarithmic at X = x1,...,xn ⊂ CP1, and flat bundles over CP1-X with integer weighted…Christian Gantz, Brian Steer·Apr 29, 1995SaveLearn
Orbifold Riemann Surfaces and the Yang-Mills-Higgs EquationsWe extend Hitchin's results on "The self-duality equations on a Riemann surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove existence results for orbifold…Ben Nasatyr, Brian Steer·Apr 26, 1995SaveLearn
Relative Geometric Invariant Theory and Universal Moduli SpacesWe expose in detail the principle that the relative geometric invariant theory of equivariant morphisms is related to the GIT for linearizations near the boundary of the G-effective ample cone. We…Yi Hu·Apr 25, 1995SaveLearn