Desingularization preserving stable simple normal crossings

详细信息    查看全文

• 作者：Edward Bierstone (1) (2)
  Franklin Vera Pacheco (1) (2)
  
  1. Department of Mathematics ; University of Toronto ; 40 St. George Street ; Toronto ; ON ; Canada ; M5S 2E4
  2. The Fields Institute ; 222 College Street ; Toronto ; ON ; Canada ; M5T 3J1
  
• 刊名：Israel Journal of Mathematics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：206
• 期：1
• 页码：233-280
• 全文大小：439 KB
• 参考文献：1. Bierstone, E., Silva, S., Milman, P. D., Vera Pacheco, F. (2014) Desingularization by blowings-up avoiding simple normal crossings. Proceedings of the American Mathematical Society 142: pp. 4099-4111 CrossRef
  2. Bierstone, E., Milman, P. D. (1989) Uniformization of analytic spaces. Journal of the American Mathematical Society 2: pp. 801-836 CrossRef
  3. Bierstone, E., Milman, P. D. (1997) Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant. Inventiones Mathematicae 128: pp. 207-302 CrossRef
  4. Bierstone, E., Milman, P. D. (2003) Desingularization algorithms I. The role of exceptional divisors. Moscow Mathematical Journal 3: pp. 751-805
  5. Bierstone, E., Milman, P. D. (2008) Functoriality in resolution of singularities. Kyoto University. Research Institute for Mathematical Sciences. Publications 44: pp. 609-639 CrossRef
  6. Bierstone, E., Milman, P. D. (2012) Resolution except for minimal singularities I. Advances in Mathematics 231: pp. 3022-3053 CrossRef
  7. Bierstone, E., Milman, P. D., Temkin, M. (2011) Q-universal desingularization. Asian Journal of Mathematics 15: pp. 229-250 CrossRef
  8. Bierstone, E., Vera Pacheco, F. (2013) Resolution of singularities of pairs preserving semisimple normal crossings. Revista de la Real Academia de Ciencias Exactas, F铆sicas y Naturales. Serie A. Matematicas. RACSAM 107: pp. 159-188
  9. O. Fujino, / Semipositivity theorems for moduli problems, preprint, arXiv:1210.5784v2 [math.AG] (2012).
  10. O. Fujino, / Vanishing theorems, in / MinimalModels and Extremal Rays, Advanced Studies in Pure Mathematics, to appear, preprint, arXiv:1202.4200v2 [math.AG] (2013).
  11. Fujino, O. (2014) Fundamental theorems for semi log canonical pairs. Algebraic Geometry 1: pp. 194-228 CrossRef
  12. J. Koll谩r, / Semi log resolutions, preprint, arXiv:0812.3592v1 [math.AG] (2008).
  13. H. Matsumura, / Commutative Algebra, Mathematics Lecture Note Series, Vol. 56, Benjamin, Reading, MA, 1980.
  14. Nobile, A. (2010) On the use of naturality in algorithmic resolution. Journal of Algebra 324: pp. 1887-1902 CrossRef
  15. Szab贸, E. (1994) Divisorial log terminal singularities. The University of Tokyo. Journal of Mathematical Sciences 1: pp. 631-639
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511

文摘

The subject is partial resolution of singularities. Given an algebraic variety X (not necessarily equidimensional) in characteristic zero (or, more generally, a pair (X, D), where D is a divisor on X), we construct a functorial desingularization of all but stable simple normal crossings (stable-snc) singularities, by smooth blowings-up that preserve such singularities. A variety has stable simple normal crossings at a point if, locally, its irreducible components are smooth and transverse in some smooth embedding variety. We also show that our main assertion is false for more general simple normal crossings singularities.