2 00 6 Disk Enumeration on the Quintic 3 - Fold

M ay 2 00 7 DISK ENUMERATION ON THE QUINTIC 3 - FOLD

Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for the disk invariants is shown to satisfy an extension of the Picard-Fuchs differential equations associated to the mirror quintic. The Ooguri-Va...

Disk Enumeration on the Quintic 3-fold

Tenth degree number fields with quintic fields having one real place

In this paper, we enumerate all number fields of degree 10 of discriminant smaller than 1011 in absolute value containing a quintic field having one real place. For each one of the 21509 (resp. 18167) found fields of signature (0, 5) (resp. (2, 4)) the field discriminant, the quintic field discriminant, a polynomial defining the relative quadratic extension, the corresponding relative discrimin...

Enumeration of N-fold Tangent Hyperplanes to a Surface

For each 1 ≤ n ≤ 6 we present formulas for the number of n−nodal curves in an n−dimensional linear system on a smooth, projective surface. This yields in particular the numbers of rational curves in the system of hyperplane sections of a generic K3−surface imbedded in IP n by a complete system of curves of genus n as well as the number 17,601,000 of rational (singular) plane quintic curves in a...

9 N ov 2 00 1 Node polynomials for families : results and examples

We continue the development of methods for enumerating nodal curves on smooth complex surfaces, stressing the range of validity. We illustrate the new methods in three important examples. First, for up to eight nodes, we confirm Göttsche's conjecture about plane curves of low degree. Second, we justify Vainsencher's enumeration of irreducible six-nodal plane curves on a general quintic threefol...