Kontsevich spaces of rational curves on Fano hypersurfaces
Kontsevich spaces of rational curves on Fano hypersurfaces
复制标题
Fano 超曲面上有理曲线的 Kontsevich 空间
DOI：
10.1515/crelle-2016-0027
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
David H Yang
中科院分区：
文献类型：
--
作者：
Eric Riedl;David H Yang
<jats:p>研究一般超曲面上的有理曲线空间。特别地，我们证明了对于一般的<jats:italic>d</jats:italic>次超曲面，<jats:inline-formula id="j_crelle-2016-0027_ineq_9999">
<jats:alternatives>
<jats:inline-graphic xlink:href="graphic/j_crelle-2016-0027_eq_0202.png" />
<jats:tex-math>{\mathbb{P}^{n}}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>与<jats:inline-formula id="j_crelle-2016-0027_ineq_9998">
<jats:alternatives>
<jats:inline-graphic xlink:href="graphic/j_crelle-2016-0027_eq_0353.png" />
<jats:tex-math>{n\geq d+2}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>空间<jats:inline-formula id="j_crelle-2016-0027_ineq_9997">
<jats:alternatives>
<jats:inline-graphic xlink:href="graphic/j_crelle-2016-0027_eq_0234.png" />
<jats:tex-math>{\overline{\mathcal{M}}_{0，0}（X，e）}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>从有理曲线到<jats:italic>X的</jats:italic><jats:italic>e次</jats:italic>Kontsevich稳定映射是维数的不可约局部完全交栈<jats:inline-formula id="j_crelle-2016-0027_ineq_9996">
<jats:alternatives>
<jats:inline-graphic xlink:href="graphic/j_crelle-2016-0027_eq_0294.png" />
<jats:tex-math>{e（n-d+1）+n-4}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>.这解决了Coskun，Harris和Starr猜想的所有情况，并且还证明了这些超曲面的Gromov-Witten不变量是枚举的。</jats:p>
<jats:p>We investigate the spaces of rational curves on a general hypersurface. In particular, we show that for a general degree <jats:italic>d</jats:italic> hypersurface in <jats:inline-formula id="j_crelle-2016-0027_ineq_9999">
<jats:alternatives>
<jats:inline-graphic xlink:href="graphic/j_crelle-2016-0027_eq_0202.png" />
<jats:tex-math>{\mathbb{P}^{n}}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> with <jats:inline-formula id="j_crelle-2016-0027_ineq_9998">
<jats:alternatives>
<jats:inline-graphic xlink:href="graphic/j_crelle-2016-0027_eq_0353.png" />
<jats:tex-math>{n\geq d+2}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>, the space <jats:inline-formula id="j_crelle-2016-0027_ineq_9997">
<jats:alternatives>
<jats:inline-graphic xlink:href="graphic/j_crelle-2016-0027_eq_0234.png" />
<jats:tex-math>{\overline{\mathcal{M}}_{0,0}(X,e)}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula> of degree <jats:italic>e</jats:italic> Kontsevich stable maps from a rational curve to <jats:italic>X</jats:italic> is an irreducible local complete intersection stack of dimension <jats:inline-formula id="j_crelle-2016-0027_ineq_9996">
<jats:alternatives>
<jats:inline-graphic xlink:href="graphic/j_crelle-2016-0027_eq_0294.png" />
<jats:tex-math>{e(n-d+1)+n-4}</jats:tex-math>
</jats:alternatives>
</jats:inline-formula>. This resolves all but one case of a conjecture of Coskun, Harris and Starr, and also proves that the Gromov–Witten invariants of these hypersurfaces are enumerative.</jats:p>
K3 曲面上的有理曲线
影响因子：
3.1
作者：
C. Liedtke
通讯作者：
C. Liedtke