Tropical geometry and the motivic nearby fiber
2011 ◽
Vol 148
(1)
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pp. 269-294
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Keyword(s):
AbstractWe 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.
2016 ◽
Vol 152
(7)
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pp. 1398-1420
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2017 ◽
Vol 153
(7)
◽
pp. 1349-1371
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2006 ◽
Vol 58
(5)
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pp. 1000-1025
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2016 ◽
Vol 68
(2)
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pp. 241-257
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Keyword(s):
2019 ◽
Vol 2019
(748)
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pp. 1-138
2011 ◽
pp. 1767-1796
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