ar X iv : s ub m it / 06 54 18 7 [ m at h . SG ] 1 4 Fe b 20 13 A natural Gromov - Witten

ar X iv : m at h / 03 02 21 1 v 1 [ m at h . A G ] 1 8 Fe b 20 03 HILBERT SCHEMES , INTEGRABLE HIERARCHIES , AND GROMOV - WITTEN THEORY

Various equivariant intersection numbers on Hilbert schemes of points on the affine plane are computed, some of which are organized into τ -functions of 2-Toda hierarchies. A correspondence between the equivariant intersection on Hilbert schemes and stationary Gromov-Witten theory is established.

ar X iv : m at h / 06 02 37 1 v 1 [ m at h . A G ] 1 7 Fe b 20 06 Braid Monodromy of Hypersurface Singularities

ar X iv : m at h / 06 02 39 4 v 1 [ m at h . G T ] 1 7 Fe b 20 06 MODULAR FIBERS AND ILLUMINATION PROBLEMS

For a Veech surface (X, ω), we characterize Aff + (X, ω) invariant subspaces of X n and prove that non-arithmetic Veech surfaces have only finitely many invariant subspaces of very particular shape (in any dimension). Among other consequences we find copies of (X, ω) embedded in the moduli-space of translation surfaces. We study illumination problems in (pre-)lattice surfaces. For (X, ω) prelat...

ar X iv : m at h / 06 02 64 7 v 1 [ m at h . A G ] 2 8 Fe b 20 06 HIGHER FANO MANIFOLDS AND RATIONAL SURFACES

Let X be a Fano manifold of pseudo-index ≥ 3 such that c 1 (X) 2 − 2c 2 (X) is nef. Irreducibility of some spaces of rational curves on X (in fact, a weaker hypothesis) implies a general point of X is contained in a rational surface.

ar X iv : 0 80 4 . 31 44 v 1 [ m at h . SG ] 1 9 A pr 2 00 8 SINGULAR SYMPLECTIC FLOPS AND RUAN COHOMOLOGY

In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient Wr = {(x, y, z, t)|xy − z + t = 0}/μr(a,−a, 1, 0), r ≥ 1, which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let X and Y be two symplectic orbifolds connected by such a flop. We study orbifold Gromov-Witten invariants of...