Martínez, César ; Sombra, Martín
Alternative Links zum Volltext:DOIVerlag
Dokumentenart: | Artikel |
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Titel eines Journals oder einer Zeitschrift: | Mathematische Zeitschrift |
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Verlag: | SPRINGER HEIDELBERG |
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Ort der Veröffentlichung: | HEIDELBERG |
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Band: | 291 |
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Nummer des Zeitschriftenheftes oder des Kapitels: | 3-4 |
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Seitenbereich: | S. 1211-1244 |
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Datum: | 2019 |
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Institutionen: | Mathematik > Prof. Dr. Walter Gubler |
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Identifikationsnummer: | Wert | Typ |
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10.1007/s00209-018-2107-0 | DOI |
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Stichwörter / Keywords: | ; Height of points; Laurent polynomials; Mixed integrals; Toric varieties; u-Resultants |
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Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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Status: | Veröffentlicht |
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Begutachtet: | Ja, diese Version wurde begutachtet |
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An der Universität Regensburg entstanden: | Ja |
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Dokumenten-ID: | 48807 |
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Zusammenfassung
We present an upper bound for the height of the isolated zeros in the torus of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions associated to the chosen height function and to the system of Laurent polynomials. We also show that this bound is close to optimal in some ...
Zusammenfassung
We present an upper bound for the height of the isolated zeros in the torus of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions associated to the chosen height function and to the system of Laurent polynomials. We also show that this bound is close to optimal in some families of examples. This result is an arithmetic analogue of the classical Berntein-Kunirenko theorem. Its proof is based on arithmetic intersection theory on toric varieties.