Birational geometry of moduli spaces of configurations of points on the line
| Autor: | Michele Bolognesi, Alex Massarenti |
|---|---|
| Přispěvatelé: | Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Divisor Moduli of curves 14D22 14H10 14H37 (Primary) 14N05 14N10 14N20 (Secondary) 01 natural sciences NO Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) PE1_4 Quotient ComputingMilieux_MISCELLANEOUS Mathematics Polynomial (hyperelastic model) Algebra and Number Theory Moduli of curves Mori dream spaces Group (mathematics) 010102 general mathematics Birational geometry 16. Peace & justice Automorphism Moduli space Cone (topology) 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Mori dream spaces |
| Zdroj: | Algebra & Number Theory Algebra & Number Theory, Mathematical Sciences Publishers 2021, 15 (2), pp.513-544. ⟨10.2140/ant.2021.15.515⟩ |
| ISSN: | 1937-0652 |
| DOI: | 10.2140/ant.2021.15.515⟩ |
| Popis: | In this paper we study the geometry of GIT configurations of $n$ ordered points on $\mathbb{P}^1$ both from the the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves of the quotient $(\mathbb{P}^1)^n//PGL(2)$, taken with the symmetric polarization, is generated by a one dimensional boundary stratum of the moduli space. Furthermore, we develop some technical machinery that we use to compute the canonical divisor and the Hilbert polynomial of $(\mathbb{P}^1)^n//PGL(2)$ in its natural embedding, and its group of automorphisms. Comment: 22 pages (fixed one small inaccuracy) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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