Yuan-Pin LeeDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112Hui-Wen LinTaida Institute of Mathematical Sciences (TIMS), National Taiwan University, Taipei 106Chin-Lung WangTaida Institute of Mathematical Sciences (TIMS), National Taiwan University, Taipei 106
For projective conifold transitions between Calabi-Yau threefolds X and Y, with X close to Y in the moduli, we show that the combined information provided by the A model (Gromov--Witten theory in all genera) and B model (variation of Hodge structures) on X, linked along the vanishing cycles, determines the corresponding combined information on Y. Similar result holds in the reverse direction when linked with the exceptional curves.
David A. CoxDepartment of Mathematics \& Computer Science, Amherst College, Amherst MA 01002Sheldon KatzDepartment of Mathematics, Oklahoma State University, Stillwater OK 74078Yuan-Pin LeeDepartment of Mathematics, University of Utah, Salt Lake City, Utah, 84112
Let V be a convex vector bundle over a smooth projective manifold X, and let Y be the subset of X which is the zero locus of a regular section of V. This mostly expository paper discusses a conjecture which relates the virtual fundamental classes of X and Y. Using an argument due to Gathmann, we prove a special case of the conjecture. The paper concludes with a discussion of how our conjecture relates to the mirror theorems in the literature.
We introduce the notion of pseudo-N´eron model and give new examples of varieties admitting pseudo-N´eron models other than Abelian varieties. As an application of pseudo-N´eron models, given a scheme admitting a finite morphism to an Abelian scheme over a positive-dimensional base, we prove that for a very general genus-0, degree-d curve in the base with d sufficiently large, every section of the scheme over the curve is contained in a unique section over the entire base.
Karl ChristBen-Gurion University of the Negev and Leibniz University HannoverXiang HeEinstein Institute of Mathematics and Yau Mathematical Sciences CenterIlya TyomkinBen-Gurion University of the Negev
Journal für die reine und angewandte Mathematik, 2022.4