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A note on discrete mixed volume and Hodge-Deligne numbers
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7186-1524
Free Univ Berlin, Berlin, Germany..
OvGU Magdeburg, Magdeburg, Germany..
2019 (English)In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 104, p. 1-13Article in journal (Refereed) Published
Abstract [en]

Generalizing the famous Bernstein-Kushnirenko theorem, Khovanskii proved in 1978 a combinatorial formula for the arithmetic genus of the compactification of a generic complete intersection associated to a family of lattice polytopes. Recently, an analogous combinatorial formula, called the discrete mixed volume, was introduced by Bihan and shown to be nonnegative. By making a footnote of Khovanskii in his paper explicit, we interpret this invariant as the (motivic) arithmetic genus of the non-compact generic complete intersection associated to the family of lattice polytopes.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2019. Vol. 104, p. 1-13
National Category
Discrete Mathematics
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URN: urn:nbn:se:kth:diva-244495DOI: 10.1016/j.aam.2018.11.002ISI: 000457668700001Scopus ID: 2-s2.0-85056843949OAI: oai:DiVA.org:kth-244495DiVA, id: diva2:1299700
Note

QC 20190328

Available from: 2019-03-28 Created: 2019-03-28 Last updated: 2019-04-04Bibliographically approved

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Di Rocco, Sandra

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