Images of Rational Maps of Projective Spaces

By Binglin Li. 2013

46 citations recorded by the source corpus.

Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the closure of the image of the rational map using a combination of techniques of moduli functors and initial degenerations. We first give a formula of multi-degree in terms of the dimensions of intersections of linear subspaces and then prove that it is Cohen-Macaulay. Finally, we compute its Hilbert polynomials.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aa03a6f990bd0190c3c6835a6f06634e0164d274

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Federico Ardila
2. Adam Boocher
3. June Huh
4. Eric Katz
5. Botong Wang

In Geometry and Topology

1. Federico Ardila
2. Adam Boocher
3. June Huh
4. Botong Wang

In Mathematical Physics

1. Federico Ardila
2. Adam Boocher
3. Eric Katz

Citations in the corpus

• The closure of a linear space in a product of lines (2013, background): “In [Li13] he computes the defining ideal and multi-degree for the closure of the image of such maps and proves that they are determined combinatorially.”