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摘要翻译：
我们考虑了所有连续映射空间中实代数簇之间的代数（正则）映射空间的包含性。对于包含实射影空间的一类实代数簇，实代数映射空间是所有连续映射空间的稠密子集。我们的第一个结果表明，对于这类变体，包含也是同伦等价的。在证明了这一点之后，我们将变体类限制在实射影空间中。在这种情况下，代数映射空间具有有限维子空间的最小次Rq滤波，随着次的增加，滤波项的同伦类型与连续映射空间的同伦类型越来越接近是很自然的。我们证明了这一点，并计算了这一近似对于这些空间的偶rq分量的下界（更准确地说，我们证明了一个非常相似和密切相关的结果，并把这个结果说成是一个猜想）。
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英文标题：
《Spaces of algebraic and continuous maps between real algebraic varieties》
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作者：
Michal Adamaszek, Andrzej Kozlowski, Kohhei Yamaguchi
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最新提交年份：
2010
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分类信息：
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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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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英文摘要：
We consider the inclusion of the space of algebraic (regular) maps between real algebraic varieties in the space of all continuous maps. For a certain class of real algebraic varieties, which include real projective spaces, it is well known that the space of real algebraic maps is a dense subset of the space of all continuous maps. Our first result shows that, for this class of varieties, the inclusion is also a homotopy equivalence. After proving this, we restrict the class of varieties to real projective spaces. In this case, the space of algebraic maps has a ` minimum degree\rq filtration by finite dimensional subspaces and it is natural to expect that the homotopy types of the terms of the filtration approximate closer and closer the homotopy type of the space of continuous mappings as the degree increases. We prove this and compute the lower bounds of this approximation for ` even\rq components of these spaces (more precisely, we prove a very similar and closely related result, and state this one as a conjecture).
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PDF链接：
https://arxiv.org/pdf/0809.4893
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