Computing Quot Schemes via Marked Bases Over Quasi-Stable Modules

Co-author(s): Mario Albert, Cristina Bertone and Margherita Roggero

Reference: Journal of Algebra, 550 (2020) 432-470

Description: We study over fields of arbitrary characteristic the definition of marked bases, a generalisation of Gröbner bases where the head terms are not necessarily chosen with respect to a term order. We assume that the head terms generate a quasi-stable module (i.e. a module possessing a Pommaret basis). Some properties of such bases are studied. In particular, we obtain upper bounds for fundamental invariants like Betti numbers, regularity or projective dimension. Furthermore, we show that the family of all ideals possessing a basis marked on the same quasi-stable module has a natural scheme structure. This allows us to compute explicit equations for Quot schemes.

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