Felipe Espreafico Guelerman - Refinements of DT invariants for Hilb Scheme of Pts in A3 - 15.06.2023

Hodge theory, Mirror Symmetry, and Physics of Calabi-Yau Moduli
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A MATCH-PIMS-STRUCTURES workshop in Mathematical Physics, held from June 12 to 16, 2023, at the Mathematikon in Heidelberg
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Abstract: We recall some relations between the Grothendieck Ring of Varieties and the Grothendieck Witt Ring of Quadratic forms and use them to get refinements of Donaldson-Thomas (DT) invariants taking values in the latter starting from the motivic DT invariants. Our main example is the case of Hilbert Schemes of points of A^3, from which we can recover real and complex invariants. We raise some questions regarding the generality of these refinements and their relationships with the literature in both A^1-enumerative geometry and in motivic DT theory. This is joint work in progress with Johannes Walcher.