论文标题
非临时证明，表明紫色等级2捆绑在投影空间上
A noncombinatorial proof that toric rank 2 bundles on projective space split
论文作者
论文摘要
Hartshorne对矢量捆绑包的猜想指出，n维投影空间上的任何等级2矢量捆绑包至少n至少为7。Klyachko已表明，当Hartshorne的猜想是当矢量捆绑包为torus earus earus equivariant时，Hartshorne的猜想是正确的。此外，Ilten和Süss的最新工作将Klyachko的工作概括为对投射空间的行为较小。在本说明中，我们给出了一个新的直接证明，表明圆环等级2捆绑包，避免了对圆环的矢量捆绑包的描述。
Hartshorne's conjecture about vector bundles on projective space states that any rank 2 vector bundle on n-dimensional projective space splits as soon as n is at least 7. Klyachko has shown that Hartshorne's conjecture is true when the vector bundles are torus equivariant. Moreover, recent work of Ilten and Süss generalizes Klyachko's work to the case of a smaller rank torus action on projective space. In this note we give a new, direct proof that torus rank 2 bundles split that avoids a description of the category of torus equivariant vector bundles.
