Exact formulas for invariants of Hilbert schemes View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-12

AUTHORS

Nate Gillman, Xavier Gonzalez, Matthew Schoenbauer

ABSTRACT

A theorem of Göttsche establishes a connection between cohomological invariants of a complex projective surface S and corresponding invariants of the Hilbert scheme of n points on S. This relationship is encoded in certain infinite product q-series which are essentially modular forms. Here we make use of the circle method to arrive at exact formulas for certain specializations of these q-series, yielding convergent series for the signature and Euler characteristic of these Hilbert schemes. We also analyze the asymptotic and distributional properties of the q-series’ coefficients. More... »

PAGES

39

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s40993-018-0132-z

DOI

http://dx.doi.org/10.1007/s40993-018-0132-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107125725


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