Enumeration of rational curves with cross-ratio constraints
详细信息 查看全文
- 作者：Ilya Tyomkin<sup>1sup><sup> ; sup><sup>tyomkin@math.bgu.ac.il" class="auth_mail" title="E-mail the corresponding authorsup>
- 关键词：Enumeration of rational curves ; Algebraic and tropical geometry
- 刊名：Advances in Mathematics
- 出版年：2017
- 出版时间：10 January 2017
- 年：2017
- 卷：305
- 期：Complete
- 页码：1356-1383
- 全文大小：604 K
文摘
In this paper we prove the algebraic–tropical correspondence for stable maps of rational curves with marked points to toric varieties such that the marked points are mapped to given orbits in the big torus and in the boundary divisor, the map has prescribed tangency to the boundary divisor, and certain quadruples of marked points have prescribed cross-ratios. In particular, our results generalize the results of Nishinou–Siebert <span id="bbr0140">[14]span>. The proof is very short, involves only the standard theory of schemes, and works in arbitrary characteristic (including the mixed characteristic case).