تقرير
Hilbert-Burch matrices and explicit torus-stable families of finite subschemes of $\mathbb A ^2$
| العنوان: | Hilbert-Burch matrices and explicit torus-stable families of finite subschemes of $\mathbb A ^2$ |
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| المؤلفون: | Oszer, Piotr |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, 14C05 (Primary), 13D02 (Secondary) |
| الوصف: | Using Hilbert-Burch matrices, we give an explicit description of the Bia{\l}ynicki-Birula cells on the Hilbert scheme of points on $\mathbb A ^2$ with isolated fixed points. If the fixed point locus is positive dimensional we obtain an \'etale rational map to the cell. We prove Conjecture 4.2 from arXiv:2309.06871 which we realize as a special case of our construction. We also show examples when the construction provides a rational \'etale map to the Hilbert scheme which is not contained in any Bia{\l}ynicki-Birula cell. Finally, we give an explicit description of the formal deformations of any ideal in the Hilbert scheme of points on the plane. Comment: Comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.07993 |
| رقم الأكسشن: | edsarx.2407.07993 |
| قاعدة البيانات: | arXiv |
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