用正特征刻画爆破下剩余阶的增长
Characterizing the increase of the residual order under blowup in positive characteristic
摘要：
在特征零中，剩余阶构成了继局部重数之后的第二个奇点奇点的分解的关键不变量。它被定义为最大切触的局部超曲面中的系数理想的阶，减去例外重数。它不会增加下爆破在允许的中心，只要当地的重数保持不变。然而，在正特征中，剩余阶（现在定义为所有光滑局部超曲面上的最大值）在爆破下可能会增加。在这篇文章中，我们详细分析了发生这种情况的情况。这可能有助于发展一个修改的剩余秩序的工作，积极的特点。
英文摘要：
In characteristic zero, the residual order constitutes, after the local multiplicity, the second key invariant for the resolution of singularities. It is defined as the order of the coefficient ideal in a local hypersurface of maximal contact, minus the exceptional multiplicities. It does not increase under blowup in permissible centers as long as the local multiplicity remains constant. In positive characteristic, however, the residual order (defined now as the maximum over all smooth local hypersurfaces) may increase under blowup. In the article we analyze in detail the circumstances when this happens. This may help to develop a modification of the residual order which does work in positive characteristic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
