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- Title
Asymptotics of random Betti tables.
- Authors
Ein, Lawrence; Erman, Daniel; Lazarsfeld, Robert
- Abstract
This paper is motivated by the question of understanding the asymptotic behavior of the Betti numbers of the resolution of the ideal of a projective variety as the positivity of the embedding line bundle grows. We present a conjecture asserting that these invariants approach a Gaussian distribution, and we verify this in the case of curves. Then we work out the asymptotics of 'random' Betti tables with a fixed number of rows, sampled according to a uniform choice of Boij-Söderberg coefficients. This analysis suggests that the normal distribution of Betti numbers is in any event the typical behavior from a probabilistic viewpoint.
- Subjects
BETTI numbers; GAUSSIAN distribution; COHOMOLOGY theory; EULER characteristic; SYZYGIES (Mathematics)
- Publication
Journal für die Reine und Angewandte Mathematik, 2015, Vol 2015, Issue 702, p55
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2013-0032