Abstract
This purely expository article is a summary of the author’s lectures on topological, algebraic, and geometric properties of the zero schemes of sections of vector bundles. These lectures were delivered at the seminar Impanga at the Banach Center in Warsaw (2006), and at the METU in Ankara (December 11–16. 2006). A special emphasis is put on the connectedness of zero schemes of sections, and the “point” and “diagonal” properties in algebraic geometry and topology. An overview of recent results by V. Srinivas, V. Pati, and the author on these properties is given.
Notes by Ozer Ozturk
Research supported by TÜBİTAK (during the stay at the METU in Ankara).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
O. Debarre, Letter to the authors of [8], 20.12.2006.
W. Fulton, Flags, Schubert polynomials, degeneracy loci, and determinantal formulas, Duke. Math. J. 65 (1992), 381–420.
W. Fulton, P. Pragacz, Schubert varieties and degeneracy loci, Lecture Notes in Math. 1689, Springer-Verlag, Berlin, 1998.
P.A. Griffiths, Hermitian differential geometry, Chern classes, and positive vector bundles, in: “Global Analysis” (D. Spencer and S. Iyanaga eds.), Princeton Math. Ser. 29, Tokyo 1969, 185–251.
A. Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France 86 (1958), 137–154.
A. Lascoux, M.-P. Schützenberger, Polynômes de Schubert, C. R. Acad. Sci. Paris 294 (1982), 447–450.
D. Mumford, Abelian varieties, Tata Inst. Studies in Math. 5, Oxford Univ. Press, 1970.
P. Pragacz, V. Srinivas, V. Pati, Diagonal subschemes and vector bundles, math.AG/0609381, to appear in the special volume of Quart. Pure Appl. Math., dedicated to Jean-Pierre Serre on his 80th Birthday.
A. Sommese, Submanifolds of abelian varieties, Math. Ann. 233 (1978), 229–256.
V. Srinivas, Some applications of algebraic cycles to affine algebraic geometry, this volume.
L. Tu, The connectedness of degeneracy loci, in: “Topics in algebra” (S. Balcerzyk et al. eds.), Banach Center Publications 26(2), Warszawa 1990, 235–248.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Pragacz, P. (2007). Miscellany on the Zero Schemes of Sections of Vector Bundles. In: Pragacz, P. (eds) Algebraic Cycles, Sheaves, Shtukas, and Moduli. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8537-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8537-8_6
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8536-1
Online ISBN: 978-3-7643-8537-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)