Asian Journal of Mathematics

Volume 23 (2019)

Number 3

Tautological systems under the conifold transition on $G(2,4)$

Pages: 501 – 526

DOI: https://dx.doi.org/10.4310/AJM.2019.v23.n3.a7

Authors

Tsung-Ju Lee (Department of Mathematics, National Taiwan University, Taipei, Taiwan)

Hui-Wen Lin (Department of Mathematics and Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taipei, Taiwan)

Abstract

Via a natural degeneration of Grassmannian manifolds $G(k, n)$ to Gorenstein toric Fano varieties $P(k, n)$ with conifold singularities, we suggest an approach to study the relation between the tautological system on $G(k, n)$ and the extended GKZ system on the small resolution $\hat{P}(k, n)$ of $P(k, n)$. We carry out the simplest case $(k, n) = (2, 4)$ to ensure its validity and show that the extended GKZ system can be regarded as a tautological system on $\hat{P}(2, 4)$.

Keywords

tautological systems, extended GKZ systems, conifold transitions, toric degenerations of Grassmannians

2010 Mathematics Subject Classification

14-xx

Received 2 February 2016

Accepted 21 February 2018

Published 9 July 2019