Tropical geometry and the motivic nearby fiber
We construct motivic invariants of a subvariety of an algebraic torus from its tropicalization and initial degenerations. More specifically, we introduce an invariant of a compactification of such a variety called the ‘tropical motivic nearby fiber’. This invariant specializes in the schön case to t...
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| Veröffentlicht in: | Compositio mathematica 2012-01, Vol.148 (1), p.269-294 |
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| container_title | Compositio mathematica |
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| creator | Katz, Eric Stapledon, Alan |
| description | We construct motivic invariants of a subvariety of an algebraic torus from its tropicalization and initial degenerations. More specifically, we introduce an invariant of a compactification of such a variety called the ‘tropical motivic nearby fiber’. This invariant specializes in the schön case to the Hodge–Deligne polynomial of the limit mixed Hodge structure of a corresponding degeneration. We give purely combinatorial expressions for this Hodge–Deligne polynomial in the cases of schön hypersurfaces and matroidal tropical varieties. We also deduce a formula for the Euler characteristic of a general fiber of the degeneration. |
| doi_str_mv | 10.1112/S0010437X11005446 |
| format | Article |
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| ispartof | Compositio mathematica, 2012-01, Vol.148 (1), p.269-294 |
| issn | 0010-437X 1570-5846 |
| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Cambridge University Press Journals Complete |
| subjects | Algebra Combinatorial analysis Construction Degeneration Fibers Geometry Invariants Mathematical analysis Polynomials |
| title | Tropical geometry and the motivic nearby fiber |
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