تقرير
On the collapsing of homogeneous bundles in arbitrary characteristic
| العنوان: | On the collapsing of homogeneous bundles in arbitrary characteristic |
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| المؤلفون: | Lőrincz, András Cristian |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, Mathematics - Representation Theory, 14M15, 14L30, 13A35, 14B05, 14M05, 20G05, 14M12 |
| الوصف: | We study the geometry of equivariant, proper maps from homogeneous bundles $G\times_P V$ over flag varieties $G/P$ to representations of $G$, called collapsing maps. Kempf showed that, provided the bundle is completely reducible, the image $G\cdot V$ of a collapsing map has rational singularities in characteristic zero. We extend this result to positive characteristic and show that for the analogous bundles the saturation $G\cdot V$ is strongly $F$-regular if its coordinate ring has a good filtration. We further show that in this case the images of collapsing maps of homogeneous bundles restricted to Schubert varieties are $F$-rational in positive characteristic, and have rational singularities in characteristic zero. We provide results on the singularities and defining equations of saturations $G\cdot X$ for $P$-stable closed subvarieties $X\subset V$. We give criteria for the existence of good filtrations for the coordinate ring of $G\cdot X$. Our results give a uniform, characteristic-free approach for the study of the geometry of a number of important varieties: multicones over Schubert varieties, determinantal varieties in the space of matrices, symmetric matrices, skew-symmetric matrices, and certain matrix Schubert varieties therein, representation varieties of radical square zero algebras (e.g. varieties of complexes), subspace varieties, higher rank varieties, etc. Comment: 22 pages. Final version, to appear in Ann. Sci. \'Ec. Norm. Sup\'er |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2008.08270 |
| رقم الأكسشن: | edsarx.2008.08270 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |