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摘要翻译：
设$(X,c_X)$是一个具有实结构的凸射影曲面。稳定映射$\bar{\mathcal{M}}_{0,k}(X，d)$的空间具有由置换群$S_k$的$C_x$和任意阶二元$\tau$作用于标记点所诱导的不同实结构。每个对应的实部$\r_{\tau}\bar{\mathcal{M}}_{0,k}(X，d)$是实正规射影簇。由于奇异轨迹的余维数大于2,因此这些空间具有第一个Stiefel-Whitney类，我们确定了在$k=C_1(X)d-1$中的一个代表，其中$C_1(X)$是$X$的第一个Chern类。即用稳定映射空间的边界因子的实部给出了这些类的同调描述。
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英文标题：
《First Stiefel-Whitney class of real moduli spaces of stable maps to a
convex surface》
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作者：
Nicolas Puignau
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Algebraic Topology 代数拓扑
分类描述：Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论，同调代数，流形的代数处理
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英文摘要：
Let $(X,c_X)$ be a convex projective surface equipped with a real structure. The space of stable maps $\bar{\mathcal{M}}_{0,k}(X,d)$ carries different real structures induced by $c_X$ and any order two element $\tau$ of permutation group $S_k$ acting on marked points. Each corresponding real part $\R_{\tau}\bar{\mathcal{M}}_{0,k}(X,d)$ is a real normal projective variety. As the singular locus is of codimension bigger than two, these spaces thus carry a first Stiefel-Whitney class for which we determine a representative in the case $k=c_1(X)d-1$ where $c_1(X)$ is the first Chern class of $X$. Namely, we give a homological description of these classes in term of the real part of boundary divisors of the space of stable maps.
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PDF链接：
https://arxiv.org/pdf/0710.2821
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