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Relevant bibliographies by topics / Birational geometry of surfaces

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Journal articles

Academic literature on the topic 'Birational geometry of surfaces'

Author: Grafiati

Published: 8 March 2025

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Journal articles on the topic "Birational geometry of surfaces"

1

Ciliberto, Ciro, Thomas Dedieu, Flaminio Flamini, and Rita Pardini. "Birational geometry of surfaces." Bollettino dell'Unione Matematica Italiana 11, no. 1 (2018): 1–3. http://dx.doi.org/10.1007/s40574-018-0157-1.

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2

Mella, Massimiliano. "Birational geometry of rational quartic surfaces." Journal de Mathématiques Pures et Appliquées 141 (September 2020): 89–98. http://dx.doi.org/10.1016/j.matpur.2020.07.007.

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3

Toda, Yukinobu. "Stability conditions and birational geometry of projective surfaces." Compositio Mathematica 150, no. 10 (2014): 1755–88. http://dx.doi.org/10.1112/s0010437x14007337.

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AbstractWe show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.

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4

Chi, Quo-Shin, Luis Fernández, and Hongyou Wu. "Normalized potentials of minimal surfaces in spheres." Nagoya Mathematical Journal 156 (1999): 187–214. http://dx.doi.org/10.1017/s0027763000007133.

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We determine explicitly the normalized potential, a Weierstrass-type representation, of a superconformal surface in an even-dimensional sphere S2n in terms of certain normal curvatures of the surface. When the Hopf differential is zero the potential embodies a system of first order equations governing the directrix curve of a superminimal surface in the twistor space of the sphere. We construct a birational map from the twistor space of S2n into ℂPn(n+1)/2. In general, birational geometry does not preserve the degree of an algebraic curve. However, we prove that the birational map preserves the degree, up to a factor 2, of the twistor lift of a superminimal surface in S6 as long as the surface does not pass through the north pole. Our approach, which is algebro-geometric in nature, accounts in a rather simple way for the aforementioned first order equations, and as a consequence for the particularly interesting class of superminimal almost complex curves in S6. It also yields, in a constructive way, that a generic superminimal surface in S6 is not almost complex and can achieve, by the above degree property, arbitrarily large area.

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5

Blanc, Jérémy, and Frédéric Mangolte. "Geometrically rational real conic bundles and very transitive actions." Compositio Mathematica 147, no. 1 (2010): 161–87. http://dx.doi.org/10.1112/s0010437x10004835.

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AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

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6

Laza, Radu, and Kieran O’Grady. "Birational geometry of the moduli space of quartic surfaces." Compositio Mathematica 155, no. 9 (2019): 1655–710. http://dx.doi.org/10.1112/s0010437x19007516.

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By work of Looijenga and others, one understands the relationship between Geometric Invariant Theory (GIT) and Baily–Borel compactifications for the moduli spaces of degree-$2$ $K3$ surfaces, cubic fourfolds, and a few other related examples. The similar-looking cases of degree-$4$ $K3$ surfaces and double Eisenbud–Popescu–Walter (EPW) sextics turn out to be much more complicated for arithmetic reasons. In this paper, we refine work of Looijenga in order to handle these cases. Specifically, in analogy with the so-called Hassett–Keel program for the moduli space of curves, we study the variation of log canonical models for locally symmetric varieties of Type IV associated to $D$-lattices. In particular, for the $19$-dimensional case, we conjecturally obtain a continuous one-parameter interpolation between the GIT and Baily–Borel compactifications for the moduli of degree-$4$ $K3$ surfaces. The analogous $18$-dimensional case, which corresponds to hyperelliptic degree-$4$ $K3$ surfaces, can be verified by means of Variation of Geometric Invariant Theory (VGIT) quotients.

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7

Morrison, David R. "The birational geometry of surfaces with rational double points." Mathematische Annalen 271, no. 3 (1985): 415–38. http://dx.doi.org/10.1007/bf01456077.

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8

Ryan, Tim, and Ruijie Yang. "Nef Cones of Nested Hilbert Schemes of Points on Surfaces." International Mathematics Research Notices 2020, no. 11 (2018): 3260–94. http://dx.doi.org/10.1093/imrn/rny088.

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Abstract Let X be the projective plane, a Hirzebruch surface, or a general K3 surface. In this paper, we study the birational geometry of various nested Hilbert schemes of points parameterizing pairs of zero-dimensional subschemes on X. We calculate the nef cone for two types of nested Hilbert schemes. As an application, we recover a theorem of Butler on syzygies on Hirzebruch surfaces.

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9

Tanaka, Hiromu. "Minimal Models and Abundance for Positive Characteristic Log Surfaces." Nagoya Mathematical Journal 216 (2014): 1–70. http://dx.doi.org/10.1215/00277630-2801646.

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AbstractWe discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for ℚ-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.

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10

Tanaka, Hiromu. "Minimal Models and Abundance for Positive Characteristic Log Surfaces." Nagoya Mathematical Journal 216 (2014): 1–70. http://dx.doi.org/10.1017/s0027763000022431.

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Abstract:

AbstractWe discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for ℚ-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.

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