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Books on the topic 'Birational geometry of surfaces'

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Published: 8 March 2025

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1

János, Kollár. Birational geometry of algebraic varieties. Cambridge: Cambridge University Press, 1998.

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2

Matsuki, Kenji. Weyl groups and birational transformations among minimal models. Providence, RI: American Mathematical Society, 1995.

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3

Kawamata, Yujiro, and Vyacheslav V. Shokurov, eds. Birational Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 1997. http://dx.doi.org/10.1090/conm/207.

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4

Brunella, Marco. Birational Geometry of Foliations. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14310-1.

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5

Hochenegger, Andreas, Manfred Lehn, and Paolo Stellari, eds. Birational Geometry of Hypersurfaces. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18638-8.

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6

Shigefumi, Mori, Miyaoka Yoichi, and Kyōto Daigaku. Sūri Kaiseki Kenkyūjo., eds. Higher dimensional birational geometry. Tokyo, Japan: Mathematical Society of Japan, 2002.

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7

Colombo, Elisabetta, Barbara Fantechi, Paola Frediani, Donatella Iacono, and Rita Pardini, eds. Birational Geometry and Moduli Spaces. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37114-2.

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8

Berenstein, Arkady, and Vladimir Retakh, eds. Noncommutative Birational Geometry, Representations and Combinatorics. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/conm/592.

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9

Cheltsov, Ivan, Ciro Ciliberto, Hubert Flenner, James McKernan, Yuri G. Prokhorov, and Mikhail Zaidenberg, eds. Automorphisms in Birational and Affine Geometry. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05681-4.

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10

Bogomolov, Fedor, Brendan Hassett, and Yuri Tschinkel, eds. Birational Geometry, Rational Curves, and Arithmetic. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6482-2.

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11

1965-, Corti Alessio, and Reid Miles, eds. Explicit birational geometry of 3-folds. Cambridge, U.K: Cambridge University Press, 2000.

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12

Cheltsov, Ivan, Xiuxiong Chen, Ludmil Katzarkov, and Jihun Park, eds. Birational Geometry, Kähler–Einstein Metrics and Degenerations. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-17859-7.

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13

Radzevich, Stephen P. Geometry of Surfaces. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-22184-3.

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14

Radzevich, Stephen P. Geometry of Surfaces. Oxford, UK: John Wiley & Sons Ltd, 2013. http://dx.doi.org/10.1002/9781118522707.

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15

Stillwell, John. Geometry of Surfaces. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-0929-4.

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16

Stillwell, John. Geometry of surfaces. New York: Springer-Verlag, 1992.

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17

Iversen, Birger. Geometry of surfaces. Aarhus: Aarhus Universitet Matematisk Institut, 1994.

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18

U, Reif, ed. Subdivision surfaces. New York: Springer, 2008.

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19

Kondō, Shigeyuki. K3 surfaces. Berlin, Germany: European Mathematical Society, 2020.

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20

Sal'kov, Nikolay. Descriptive geometry: Designing surfaces. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1196545.

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In the textbook, in addition to the geometric design of surfaces, the elements of analytical and parametric geometries are proposed that contribute to the design and bring the result to a higher level of knowledge, as well as a frame method for designing surfaces. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of the specialties "Architect" and " Designer of the architectural environment "(qualifications "bachelor", "specialist", "master"). It may be useful for students of other fields of study.

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21

Gardiner, Frederick P., Gabino Gonzalez-Diez, and Christos Kourouniotis, eds. Geometry of Riemann Surfaces. Cambridge: Cambridge University Press, 2009. http://dx.doi.org/10.1017/cbo9781139194266.

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22

Grima, Clara I., and Alberto Márquez. Computational Geometry on Surfaces. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9809-5.

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23

service), SpringerLink (Online, ed. Algebraic Surfaces. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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24

A, Iskovskikh V., Shokurov Vyacheslav V. 1950-, and Shokurov Vyacheslav V. 1950-, eds. Birational geometry: Linear systems and finitely generated algebras : collected papers. Moscow, Russia: Maik Nauka/Interperiodica, 2003.

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25

A, Iskovskikh V., Shokurov Vyacheslav V. 1950-, and Shokurov Vyacheslav V. 1950-, eds. Birational geometry: Linear systems and finitely generated algebras : collected papers. Moscow, Russia: Maik Nauka/Interperiodica, 2003.

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26

Arkady, Berenstein, and Retakh Vladimir, eds. Noncommutative birational geometry, representations and combinatorics: AMS Special Session on Noncommutative Birational Geometry, Representations and Cluster Algebras, January 6-7, 2012, Boston, MA. Providence, Rhode Island: American Mathematical Society, 2013.

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27

Montiel, Sebastián. Curves and surfaces. Providence, R.I: American Mathematical Society, 2005.

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28

Pfahler, Eisenhart Luther. Riemannian geometry. Princeton, N.J: Princeton University Press, 1997.

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29

Baader, Sebastian. Geometry and topology of surfaces. Berlin, Germany: EMS Press, 2021.

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30

D, Burago I͡U︡, and Zalgaller V. A, eds. Geometry III: Theory of surfaces. Berlin: Springer-Verlag, 1992.

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31

Kuhnel, Wolfgang. Differential geometry: Curves - surfaces - manifolds. 2nd ed. Providence, RI: American Mathematical Society, 2006.

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32

Kühnel, Wolfgang. Differential geometry: Curves, surfaces, manifolds. Providence, Rhode Island: American Mathematical Society, 2015.

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33

Baader, Sebastian. Geometry and topology of surfaces. Berlin: EMS Press, 2021.

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34

Marcel, Berger. Differential geometry: Manifolds, curves, and surfaces. New York: Springer-Verlag, 1988.

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35

Lastra, Alberto. Parametric Geometry of Curves and Surfaces. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81317-8.

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36

Kobayashi, Shoshichi. Differential Geometry of Curves and Surfaces. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-1739-6.

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37

Tapp, Kristopher. Differential Geometry of Curves and Surfaces. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-39799-3.

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38

Corti, Alessio, and Miles Reid. Explicit Birational Geometry Of 3-Folds. Cambridge University Press, 2000.

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39

Corti, Alessio, and Miles Reid. Explicit Birational Geometry Of 3-Folds. Cambridge University Press, 2013.

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40

Corti, Alessio, and Miles Reid. Explicit Birational Geometry Of 3-Folds. Cambridge University Press, 2013.

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41

Birational Geometry of Algebraic Varieties Cambridge Tracts in Mathematics Paperback. Cambridge University Press, 2008.

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42

Tretkoff, Paula. Algebraic Surfaces and the Miyaoka-Yau Inequality. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0005.

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This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally equivalent to a smooth surface containing no exceptional curves. The latter is known as a minimal surface. Two related birational invariants, the plurigenus and the Kodaira dimension, play an important role in distinguishing between complex surfaces. The chapter first provides an overview of the rough classification of (smooth complex connected compact algebraic) surfaces before presenting two approaches that, in dimension 2, give the Miyaoka-Yau inequality. The first, due to Miyaoka, uses algebraic geometry, whereas the second, due to Aubin and Yau, uses analysis and differential geometry. The chapter also explains why equality in the Miyaoka-Yau inequality characterizes surfaces of general type that are free quotients of the complex 2-ball.

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43

Park, Jihun, and Ivan Cheltsov. Birationally Rigid Fano Threefold Hypersurfaces. American Mathematical Society, 2017.

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44

Surveys on Recent Developments in Algebraic Geometry. American Mathematical Society, 2017.

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45

Brunella, Marco. Birational Geometry of Foliations. Springer, 2015.

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46

Brunella, Marco. Birational Geometry of Foliations. Springer, 2015.

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47

Brunella, Marco. Birational Geometry of Foliations. Springer, 2016.

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48

Birational geometry of foliations. IMPA, 2009.

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49

Kollár, Janos, and Shigefumi Mori. Birational Geometry of Algebraic Varieties. Cambridge University Press, 2010.

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50

Colombo, Elisabetta, Barbara Fantechi, Rita Pardini, Paola Frediani, and Donatella Iacono. Birational Geometry and Moduli Spaces. Springer, 2020.

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