When are multidegrees positive? -- Jonathan MontaƱo, July 29, 2020.

Abstract: Let k be an arbitrary field, P a multiprojective space over k, and X a closed subscheme of P. The multidegrees of X are the analogues of the notion of degree in the multiprojective setting and are fundamental invariants that describe algebraic and geometric properties of X. In this talk we present recent results that provide necessary and sufficient conditions for the positivity of the multidegrees of X. As a consequence of our methods, we show that when X is irreducible, the support of multidegrees forms a discrete algebraic polymatroid. This is joint work with Federico Castillo,Yairon Cid-Ruiz, Binglin Li, and Naizhen Zhang.