Using stacks to impose tangency conditions on curves

2007/04/01 by Charles Cadman · 4 citations
Mathematics · Chemistry · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Axial and Atropisomeric Chirality Synthesis #Mathematics #Divisor (algebraic geometry) #Stack (abstract data type) #Moduli #Tangent #Integer (computer science) #Scheme (mathematics) #Pure mathematics #Combinatorics #Mathematical analysis #Geometry #Physics #Computer science

paper · pdf · doi:10.1353/ajm.2007.0007

openalex publication_date 2007/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We define a Deligne-Mumford stack XD,r which depends on a scheme X, an effective Cartier divisor D ⊂ X, and a positive integer r. Then we show that the Abramovich-Vistoli moduli stack of stable maps into XD,r provides compactifications of the locally closed substacks of M g,n(X, β) corresponding to relative stable maps.

Citations

• Contact formulas for rational plane curves via stable maps
• Éléments de géométrie algébrique : IV. Étude locale des schémas et des morphismes de schémas, Première partie

Cited by

• Pullback of parabolic bundles and covers of ℙ1\0,1,∞
• Semistability criterion for parabolic vector bundles on curves
• Stack structures on GIT quotients parametrizing hypersurfaces
• Gerbe [wikipedia]