2013/07/21 by Pinaki Mondal, Mondal, Pinaki
Mathematics · #14J26 #14L30 #14M27 #32C15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.1307.5577
openalex publication_date 2013/07/21 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
We classify 'primitive normal compactifications' of C2 (i.e. normal analytic\nsurfaces containing C2 for which the curve at infinity is irreducible),\ncompute the moduli space of these surfaces and their groups of auomorphisms. In\nparticular we show that in 'most' of these surfaces C2 is 'rigidly embedded'.\nAs an application we give a description of 'embedded isomorphism classes' of\nplanar curves with one place at infinity. We also compute the canonical divisor\nof these surfaces; it turns out that their log discrepancy is related to the\nFrobenius number of the semigroup of poles along the curve at infinity. We use\nthe computation to classify Gorenstein primitive compactifications of C2 with\nrational and minimally elliptic singularities, extending a result of Brenton,\nDrucker and Prins (Ann. of Math. Stud., vol 100, 1981). As another application\nwe characterize weighted projective spaces of the form P2(1,1,q) in terms of\ntheir 'log discrepancy' and 'index', generalizing a characterization of P2 due\nto Borisov (Journal of Algebraic Combinatorics, 2014).\n