Making enumerative predictions by means of mirror symmetryGiven two Calabi--Yau threefolds which are believed to constitute a mirror pair, there are very precise predictions about the enumerative geometry of rational curves on one of the manifolds which can…David R. Morrison·Apr 24, 1995SaveLearn
On irreducible four--manifoldsWe show that minimal symplectic 4--manifolds with b2+ >1 and with residually finite fundamental groups are irreducible. We also give examples of irreducible orientable four--manifolds with…D. Kotschick·Apr 23, 1995SaveLearn
Picard groups of the moduli spaces of vector bundles over algebraic surfacesWe determined the Picard group of the moduli of rank two stable sheaves on an arbitrary algebraic surface up to finite indexJun Li·Apr 16, 1995SaveLearn
The first two Betti numbers of the moduli spaces of vector bundles on surfacesWe determined the first two Betti numbers of the moduli of rank two stable sheaves on an arbitrary algebraic surfaceJun Li·Apr 16, 1995SaveLearn
The quantum cohomology of homogeneous varietiesWe established the associativity of the quantum cohomologies of homogeneous varieties by using degeneration method in algebraic geometry.Jun Li, Gang Tian·Apr 16, 1995SaveLearn
Integral Subschemes of Codimension TwoIn this paper we study the problem of describing the integral subschemes within a fixed even linkage class Ł of subschemes in of codimension two. In the case that Ł is not the class of…Scott Nollet·Apr 15, 1995SaveLearn
Some Donaldson invariants of CP2We compute the Donaldson numbers q17(CP2)=2540 and q21(CP2)=233208.Geir Ellingsrud, Joseph Le Potier, Stein A. Stromme·Apr 13, 1995SaveLearn
Siegel automorphic form corrections of some Lorentzian Kac--Moody Lie algebrasWe find automorphic form corrections which are generalized Lorentzian Kac--Moody superalgebras without odd real simple roots (see R. Borcherds Bo1 -- Bo7, V. Kac Ka1 --…Valeri A. Gritsenko, Viacheslav V. Nikulin·Apr 10, 1995SaveLearn
Intersection-theoretical computations onWe determine necessary conditions for ample divisors in arbitrary genus as well as for very ample divisors in genus 2 and 3. We also compute the intersection numbers λ9 and λg-13 in genus 4.…Carel Faber·Apr 6, 1995SaveLearn
Intersections of Q-Divisors on Kontsevich's Moduli Space M0,n(Pr,d) and Enumerative GeometryThe theory of Q-Cartier divisors on the space of n-pointed, genus 0, stable maps to projective space is considered. Generators and Picard numbers are computed. A recursive algorithm computing all top…R. Pandharipande·Apr 6, 1995SaveLearn
Severi Degrees in Cogenus 3In this short note, a new computation of the degree of the locus of 3-nodal plane curves in the linear system of degree d plane curves is given. The answer is expressed as a tautological class on a…J. Harris, R. Pandharipande·Apr 6, 1995SaveLearn
On number of hypersurfaces containing projective curvesGeneralizing a classical lemma of Castelnuovo, we characterize rational normal curves (resp. linearly normal elliptic curves) as curves C⊂ n such that the number of linearly independent…S. L'vovsky·Apr 4, 1995SaveLearn
Hyperbolic PlanesIn this paper we consider a special class of arithmetic quotients of bounded symmetric domains which can roughly be described as higher- dimensional analogues of the Hilbert modular varities. The…Bruce Hunt·Apr 3, 1995SaveLearn
Local Homology and Cohomology on SchemesWe prove a sheaf-theoretic derived-category generalization of Greenlees-May duality (a far-reaching generalization of Grothendieck's local duality theorem): for a quasi-compact separated scheme X…Leovigildo Alonso, Ana Jeremías, Joseph Lipman·Mar 30, 1995SaveLearn
The Mumford relations and the moduli of rank three stable bundlesWe find a complete set of relations for the rational cohomology ring of the moduli space of rank three stable bundles over a Riemann surface of genus g and also show that the Pontryagin ring vanishes…Richard Earl·Mar 29, 1995SaveLearn
Degrees of generators of ideals defining subschemes of projective spaceFor an arithmetically Cohen--Macaulay subscheme of projective space, there is a well-known bound for the highest degree of a minimal generator for the defining ideal of the subscheme, in terms of the…Heath M. Martin, Juan C. Migliore·Mar 29, 1995SaveLearn
Roitman's theorem for singular complex projective surfacesLet X be a complex projective surface with arbitrary singularities. We construct a generalized Abel--Jacobi map A0(X) J2(X) and show that it is an isomorphism on torsion subgroups. Here…L. Barbieri-Viale, C. Pedrini, C. Weibel·Mar 29, 1995SaveLearn
Théorèmes De Connexité Pour Les Produits D'Espaces Projectifs et Les GrassmanniennesLet G be the Grassmannian G(d,n), let X and Y be complete irreducible varieties, and let X→ G and Y→ G be morphisms. Hansen proved that X ×G Y is connected…Olivier Debarre·Mar 28, 1995SaveLearn
Moduli of pre- D-modules, perverse sheaves and the Riemann-Hilbert morphism -IWe construct a moduli scheme for semistable pre--modules with prescribed singularities and numerical data on a smooth projective variety. These pre--modules are to be viewed as regular…Nitin Nitsure, Claude Sabbah·Mar 28, 1995SaveLearn
An orbifold partition of MgnWe define a partition of Mgn and show that the cohomology of Mgn in a given degree admits a filtration whose respective quotients are isomorphic to the shifted…Martin Pikaart·Mar 27, 1995SaveLearn
A gem of the modular universeWe introduce one of the most beautiful algebraic varieties known, a quintic hypersurface in projective five-space, which is invariant under the action of the Weyl group of E6. This variety is…Bruce Hunt·Mar 27, 1995SaveLearn
Akizuki's counterexampleFollowing Akizuki, I construct a Noetherian local integral domain CM whose normalisation (integral closure) is not finite over CM. My proof follows closely Akizuki's ingenious calculations.Miles Reid·Mar 26, 1995SaveLearn
On a conjecture of VarchenkoIn this note we generalize and prove a recent conjecture of Varchenko concerning the number of critical points of a (multivalued) meromorphic function ϕ on an algebraic manifold. Under certain…Roberto Silvotti·Mar 26, 1995SaveLearn
The nil Hecke ring and singularity of Schubert varietiesWe give a criterion for smoothness of a point in any Schubert variety in any G/B in terms of the nil Hecke ring.Shrawan Kumar·Mar 24, 1995SaveLearn
Stable Parabolic Bundles over Elliptic Surfaces and over Orbifold Riemann SurfacesFor an elliptic surface q:Y Σ, with prescribed singular fibres, Stefan Bauer proved directly via algebraic geometry that the stable bundles over Y, whose chern classes are pull backs from…Christian Gantz, Brian Steer·Mar 22, 1995SaveLearn