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math.AC2022
Ideals of submaximal minors of sparse symmetric matrices
Jiahe Deng, Andreas Kretschmer
We study algebraic and homological properties of the ideal of submaximal minors of a sparse generic symmetric matrix. This ideal is generated by all -minors of a symmetric $…
math.CO2022
Thin polytopes: Lattice polytopes with vanishing local -polynomial
Christopher Borger, Andreas Kretschmer, Benjamin Nill
In this paper we study the novel notion of thin polytopes: lattice polytopes whose local -polynomials vanish. The local -polynomial is an important invariant in modern Eh…
math.AG2022
The enumerative geometry of cubic hypersurfaces: point and line conditions
Mara Belotti, Alessandro Danelon, Claudia Fevola +1
In order to count the number of smooth cubic hypersurfaces tangent to a prescribed number of lines and passing through a given number of points, we construct a compactification of…