Rigid divisors on surfaces
- Authors: Hochenegger A.1, Ploog D.2
-
Affiliations:
- Scuola Normale Superiore
- University of Stavanger
- Issue: Vol 84, No 1 (2020)
- Pages: 163-206
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133804
- DOI: https://doi.org/10.4213/im8721
- ID: 133804
Cite item
Open Access
Access granted
Subscription Access
Abstract
We study effective divisors $D$ on surfaces with $H^0(\mathcal{O}_D)=\Bbbk$and $H^1(\mathcal{O}_D)=H^0(\mathcal{O}_D(D))=0$. We give a numerical criterionfor such divisors, following a general investigation of negativity, rigidity and connectivityproperties. Examples include exceptional loci of rational singularities, and spherelikedivisors.
About the authors
Andreas Hochenegger
Scuola Normale SuperiorePhD, Researcher
David Ploog
University of StavangerDoctor of physico-mathematical sciences
References
- R. Lazarsfeld, Positivity in algebraic geometry, v. I, Ergeb. Math. Grenzgeb. (3), 48, Classical setting: line bundles and linear series, Springer-Verlag, Berlin, 2004, xviii+387 pp.
- Th. Bauer, B. Harbourne, A. L. Knutsen, A. Küronya, S. Müller-Stach, X. Roulleau, T. Szemberg, “Negative curves on algebraic surfaces”, Duke Math. J., 162:10 (2013), 1877–1894
- A. Hochenegger, M. Kalck, D. Ploog, “Spherical subcategories in algebraic geometry”, Math. Nachr., 289:11-12 (2016), 1450–1465
- У. Фултон, Теория пересечений, Мир, М., 1989, 583 с.
- Р. Хартсхорн, Алгебраическая геометрия, Мир, М., 1981, 600 с.
- M. Reid, “Chapters on algebraic surfaces”, Complex algebraic geometry (Park City, UT, 1993), IAS/Park City Math. Ser., 3, Amer. Math. Soc., Providence, RI, 1997, 3–159
- D. Huybrechts, Fourier–Mukai transforms in algebraic geometry, Oxford Math. Monogr., The Clarendon Press, Oxford Univ. Press, Oxford, 2006, viii+307 pp.
- W. P. Barth, K. Hulek, C. A. M. Peters, A. Van de Ven, Compact complex surfaces, Ergeb. Math. Grenzgeb. (3), 4, 2nd ed., Springer-Verlag, Berlin, 2004, xii+436 pp.
- L. Hille, D. Ploog, “Tilting chains of negative curves on rational surfaces”, Nagoya Math. J., 235 (2019), 26–41
- D. Vossieck, “The algebras with discrete derived category”, J. Algebra, 243:1 (2001), 168–176
- G. Bobinski, C. Geiss, A. Skowronski, “Classification of discrete derived categories”, Cent. Eur. J. Math., 2:1 (2004), 19–49
- L. Hille, D. Ploog, “Exceptional sequences and spherical modules for the Auslander algebra of $k[x]/(x^t)$”, Pacific J. Math., 302:2 (2019), 599–625
- A. Hochenegger, M. Kalck, D. Ploog, “Spherical subcategories in representation theory”, Math. Z., 291:1-2 (2019), 113–147
- M. Artin, “Some numerical criteria for contractability of curves on algebraic surfaces”, Amer. J. Math., 84:3 (1962), 485–496
- M. Artin, “On isolated rational singularities of surfaces”, Amer. J. Math., 88 (1966), 129–136
- L. Bădescu, Algebraic surfaces, Transl. from the Romanian, Universitext, Springer-Verlag, New York, 2001, xii+258 pp.
- Г. Грауэрт, “О модификациях и исключительных аналитических множествах”, Комплексные пространства, Cб. пер., Мир, М., 1965, 45–104
- R. S. Varga, Matrix iterative analysis, Springer Ser. Comput. Math., 27, 2nd rev. and exp. ed., Springer-Verlag, Berlin, 2000, x+358 pp.
- E. R. Garcia Barroso, P. D. Gonzalez Perez, P. Popescu-Pampu, “Ultrametric spaces of branches on arborescent singularities”, Singularities, algebraic geometry, commutative algebra and related topics, Springer, Cham, 2018, 55–106
- A. H. Durfee, “Fifteen characterizations of rational double points and simple critical points”, Enseign. Math. (2), 25:1-2 (1979), 131–163
- H. B. Laufer, “On rational singularities”, Amer. J. Math., 94:2 (1972), 597–608
- A. Nemethi, “Five lectures on normal surface singularities”, Low dimensional topology (Eger, 1996/Budapest, 1998), Bolyai Soc. Math. Stud., 8, Janos Bolyai Math. Soc., Budapest, 1999, 269–351
Supplementary files
