Abundance of 3-Planes on Real Projective Hypersurfaces

2015-07-01
© 2015, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.We show that a generic real projective n-dimensional hypersurface of odd degree d, such that 4(n-2)=(d+33), contains “many” real 3-planes, namely, in the logarithmic scale their number has the same rate of growth, d3log d, as the number of complex 3-planes. This estimate is based on the interpretation of a suitable signed count of the 3-planes as the Euler number of an appropriate bundle.
Arnold Mathematical Journal

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Citation Formats
S. Finashin, “Abundance of 3-Planes on Real Projective Hypersurfaces,” Arnold Mathematical Journal, vol. 1, no. 2, pp. 171–199, 2015, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/92625.