Algebraic cobordism revisited |
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Authors: | Email author" target="_blank">M?LevineEmail author R?Pandharipande |
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Institution: | (1) Department of Mathematics, Northeastern University, 360 Huntington Ave., Boston, MA 02115, USA;(2) Department of Mathematics, Princeton University, Princeton, NJ 08544, USA |
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Abstract: | We define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities.
The main result is the equivalence of double point cobordism to the theory of algebraic cobordism previously defined by Levine
and Morel. Double point cobordism provides a simple, geometric presentation of algebraic cobordism theory. As a corollary,
the Lazard ring given by products of projective spaces rationally generates all nonsingular projective varieties modulo double
point degenerations.
Double point degenerations arise naturally in relative Donaldson–Thomas theory. We use double point cobordism to prove all
the degree 0 conjectures in Donaldson–Thomas theory: absolute, relative, and equivariant. |
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Keywords: | |
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