30 citations · 40 across the 4 of their papers we have counts for
6 papers
Virtual fundamental classes, global normal cones and Fulton's canonical classes
Bernd Siebert
This paper, first written in 1997, aims at a simplified and more elementary construction of algebraic-geometric virtual fundamental classes as defined by Li/Tian and Behrend/Fantec…
Toric degenerations of toric varieties and tropical curves
Takeo Nishinou, Bernd Siebert
We show that the counting of rational curves on a complete toric variety that are in general position to the toric prime divisors coincides with the counting of certain tropical cu…
Mirror Symmetry via Logarithmic Degeneration Data I
Mark Gross, Bernd Siebert
This paper is the first arising from our project announced in math.AG/0211094, "Affine manifolds, log structures, and mirror symmetry." We aim to study mirror symmetry by studying…
On the holomorphicity of genus two Lefschetz fibrations
Bernd Siebert, Gang Tian
We prove that any genus-2 Lefschetz fibration without reducible fibers and with ``transitive monodromy'' is holomorphic. The latter condition comprises all cases where the number o…
On hyperelliptic -Lefschetz fibrations of four-manifolds
B. Siebert, G. Tian
We show that hyperelliptic symplectic Lefschetz fibrations are symplectically birational to two-fold covers of rational ruled surfaces, branched in a symplectically embedded surfac…
Algebraic and symplectic Gromov-Witten invariants coincide
Bernd Siebert
For a complex projective manifold Gromov-Witten invariants can be constructed either algebraically or symplectically. Using the versions of Gromov-Witten theory by Behrend and Fant…