تقرير
Jacobian schemes arising from hypersurface arrangements in $\mathbb P^n$
| العنوان: | Jacobian schemes arising from hypersurface arrangements in $\mathbb P^n$ |
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| المؤلفون: | Migliore, Juan, Nagel, Uwe |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, 14N20, 14M05, 14M06, 32S22, 13C40, 13H10 |
| الوصف: | Freeness is an important property of a hypersurface arrangement, although its presence is not well understood. A hypersurface arrangement in $\PP^n$ is free if $S/J$ is Cohen-Macaulay (CM), where $S = K[x_0,\ldots,x_n]$ and $J$ is the Jacobian ideal. We study three related unmixed ideals: $J^{top}$, the intersection of height two primary components, $\sqrt{J^{top}}$, the radical of $J^{top}$, and when the $f_i$ are smooth we also study $\sqrt{J}$. Under mild hypotheses, we show that these ideals are CM. This establishes a full generalization of an earlier result with Schenck from hyperplane arrangements to hypersurface arrangements. If the hypotheses fail for an arrangement in projective $3$-space, the Hartshorne-Rao module measures the failure of CMness. We establish consequences for the even liaison classes of $J^{top}$ and $\sqrt{J}$. Comment: Slightly revised and corrected statement of main theorem. To appear in IMRN |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.01192 |
| رقم الأكسشن: | edsarx.2312.01192 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |