Enumerative geometry with quadratic forms
Principal Investigator
Prof. Dr. M. Levine (Essen)Scientific Staff
Enzo Serandon (Essen 1.1.20-3.31.22)
Pietro Gigli (Essen 01.01.2021-31.10.2022)
Project description
The main goals of this project are to use motivic homotopy theory to develop methods suitable for the construction of a theory of enumerative geometry with values in quadratic forms, to apply these methods to key problems in enumerative geometry, and to use the resulting quadratic invariants to give a deeper understanding of the enumerative geometry of real varieties as well as the arithmetic aspects of enumerative problems over an arbitrary field.Related publications
Published articles
Marc Levine. Aspects of enumerative geometry with quadratic forms. Doc. Math. 25 (2020), 2179--2239.
Marc Levine, Arpon Raksit. Motivic Gauss-Bonnet formulas. Algebra Number Theory 14 (2020), no. 7, 1801--1851.
Marc Levine. The intrinsic stable normal cone. Algebr. Geom. 8 (2021), no. 5, 518--561.
Marc Levine. Lectures on quadratic enumerative geometry. `` Motivic homotopy theory and refined enumerative geometry'', 163--198, Contemp. Math., 745, Amer. Math. Soc., RI, [2020].
Preprints
Marc Levine, Toward an algebraic theory of Welschinger invariants. Preprint 2018 arXiv:1808.02238.