On the multigraded Hilbert function of lines and rational curves in multiprojective spaces. (English) Zbl 1510.14037
Summary: We study the multigraded Hilbert function of general configurations of lines in multiprojective spaces. In several cases we prove that this multigraded Hilbert function is the expected one. We make conjectures about other configurations and for small genus curves with a prescribed multidegree.
MSC:
| 14N05 | Projective techniques in algebraic geometry |
| 14H50 | Plane and space curves |
| 13D40 | Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series |
Keywords:
Segre varieties; multiprojective spaces; lines; Hilbert function; multigraded Hilbert function; Segre-Veronese varietiesReferences:
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