The Fulton-MacPherson compactification is not a Mori dream space
Patricio Gallardo, Jos\'e Luis Gonz\'alez, Evangelos Routis
TL;DR
The paper proves that the Fulton-MacPherson compactification of configuration spaces is not a Mori dream space for sufficiently large numbers of points, specifically when n exceeds d+8, in various varieties including projective space.
Contribution
It establishes the non-Mori dream space property of Fulton-MacPherson compactifications for large n, extending understanding of their geometric complexity.
Findings
Fulton-MacPherson compactification is not a Mori dream space for n > d+8.
This result applies to configuration spaces in projective space and other varieties.
The work highlights limitations in the algebraic structure of these compactifications.
Abstract
We show that the Fulton-MacPherson compactification of the configuration space of distinct labeled points in certain varieties of arbitrary dimension , including projective space, is not a Mori dream space for larger than .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology