ar X iv : a lg - g eo m / 9 60 40 19 v 1 2 8 A pr 1 99 6 RECURSIVE FORMULAS FOR THE CHARACTERISTIC NUMBERS OF RATIONAL PLANE CURVES

ar X iv : a lg - g eo m / 9 60 80 25 v 1 2 2 A ug 1 99 6 COUNTING PLANE CURVES OF ANY GENUS

ar X iv : a lg - g eo m / 9 70 70 16 v 1 2 5 Ju l 1 99 7 RATIONAL CURVES ON QUASI - PROJECTIVE SURFACES

§

ar X iv : a lg - g eo m / 9 60 30 11 v 1 1 4 M ar 1 99 6 The Hilbert Schemes of Degree Three Curves are Connected

In this paper we show that the Hilbert scheme H(3, g) of locally Cohen-Macaulay curves in P of degree three and genus g is connected. This is achieved by giving a classification of these curves, determining the irreducible components of H(3, g), and giving certain specializations to show connectedness. As a byproduct, we find that there are curves which lie in the closure of each irreducible co...

ar X iv : a lg - g eo m / 9 60 20 19 v 1 2 7 Fe b 19 96 FORMULAS FOR LAGRANGIAN AND ORTHOGONAL DEGENERACY LOCI ; The Q̃ - Polynomials Approach

Introduction 1. Schubert subschemes and their desingularizations. 2. Isotropic Schubert calculus and the class of the diagonal. 3. Subbundles intersecting an n-subbundle in dim > k. 4. Q̃-polynomials and their properties. 5. Divided differences and isotropic Gysin maps; orthogonality of Q̃-polynomials. 6. Single Schubert condition. 7. Two Schubert conditions. 8. An operator proof of Proposition 3...

ar X iv : a lg - g eo m / 9 70 30 13 v 1 1 0 M ar 1 99 7 CONTACT COHOMOLOGY OF THE PROJECTIVE PLANE

In this paper, we construct an associative ring which we call the contact cohomology ring of the projective plane. The construction should work for other varieties, including projective spaces of all dimensions, but we restrict ourselves to this example both for clarity of exposition and because we rely on certain technical results from our earlier paper [EK96]. As we formulate it in section 3 ...