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322
Fixing all moduli in a simple Ftheory compactification,” [arXiv:hepth/0503124
"... We discuss a simple example of an Ftheory compactification on a CalabiYau fourfold where background fluxes, nonperturbative effects from Euclidean D3 instantons and gauge dynamics on D7 branes allow us to fix all closed and open string moduli. We explicitly check that the known higher order correc ..."
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Cited by 91 (8 self)
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We discuss a simple example of an Ftheory compactification on a CalabiYau fourfold where background fluxes, nonperturbative effects from Euclidean D3 instantons and gauge dynamics on D7 branes allow us to fix all closed and open string moduli. We explicitly check that the known higher order corrections to the potential, which we neglect in our leading approximation, only shift the results by a small amount. In our exploration of the model, we encounter interesting new phenomena, including examples of transitions where D7 branes absorb O3 planes, while changing topology to preserve the net D3 charge.
A simply connected surface of general type with pg = 0 and K² = 2
, 2007
"... In this paper we construct a simply connected, minimal, complex surface of general type with pg = 0 and K² = 2 using a rational blowdown surgery and a QGorenstein smoothing theory. ..."
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Cited by 55 (8 self)
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In this paper we construct a simply connected, minimal, complex surface of general type with pg = 0 and K² = 2 using a rational blowdown surgery and a QGorenstein smoothing theory.
Introduction to the log minimal model program for log canonical pairs
, 2009
"... We describe the foundation of the log minimal model program for log canonical ..."
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Cited by 47 (18 self)
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We describe the foundation of the log minimal model program for log canonical
On the Geometry of SasakianEinstein 5Manifolds
 MATH. ANN
"... On simply connected five manifolds SasakianEinstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for threebrane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kollar [DK] a ..."
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Cited by 45 (17 self)
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On simply connected five manifolds SasakianEinstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for threebrane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kollar [DK] and Johnson and Kollar [JK1] who give methods for constructing KahlerEinstein metrics on log del Pezzo surfaces. By [BG1] circle Vbundles over log del Pezzo surfaces with KahlerEinstein metrics have SasakianEinstein metrics on the total space of the bundle. Here these simply connected 5manifolds arise as links of isolated hypersurface singularities which by the well known work of Smale [Sm] together with [BG3] must be diffeomorphic to S 5
The Kodaira dimension of moduli spaces of curves with marked points
"... Abstract. We sharpen our previous results on the g and n such that Mg,n is of general type for some g with g + 1 prime. 1. Introduction. This ..."
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Cited by 42 (0 self)
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Abstract. We sharpen our previous results on the g and n such that Mg,n is of general type for some g with g + 1 prime. 1. Introduction. This
Compact moduli of plane curves
, 2004
"... We construct a compactification Md of the moduli space of plane curves of degree d. We regard a plane curve C ⊂ P 2 as a surfacedivisor pair (P 2, C) and define Md as a moduli space of pairs (X, D) where X is a degeneration of the plane. We show that, if d is not divisible by 3, the stack Md is smo ..."
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Cited by 39 (6 self)
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We construct a compactification Md of the moduli space of plane curves of degree d. We regard a plane curve C ⊂ P 2 as a surfacedivisor pair (P 2, C) and define Md as a moduli space of pairs (X, D) where X is a degeneration of the plane. We show that, if d is not divisible by 3, the stack Md is smooth and the degenerate surfaces X can be described explicitly.
MIRROR SYMMETRY FOR LOG CALABIYAU SURFACES I
, 2011
"... We give a canonical synthetic construction of the mirror family to a pair (Y,D) of a smooth projective surface with an anticanonical cycle of rational curves, as the spectrum of an explicit algebra defined in terms of counts of rational curves on Y meeting D in a single point. In the case D is con ..."
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Cited by 36 (7 self)
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We give a canonical synthetic construction of the mirror family to a pair (Y,D) of a smooth projective surface with an anticanonical cycle of rational curves, as the spectrum of an explicit algebra defined in terms of counts of rational curves on Y meeting D in a single point. In the case D is contractible, the family gives a smoothing of the dual cusp, and thus a proof of Looijenga’s 1981 cusp conjecture.
Birational geometry of terminal quartic 3folds
 I, Amer. J. Math
"... 1.1. Abstract. In this paper, we study the birational geometry of certain examples of mildly singular quartic 3folds, a small step inside a larger program of research. A quartic 3fold is an example of a Fano variety, that is, a variety X with ample anticanonical sheaf OX(−KX). ..."
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Cited by 36 (2 self)
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1.1. Abstract. In this paper, we study the birational geometry of certain examples of mildly singular quartic 3folds, a small step inside a larger program of research. A quartic 3fold is an example of a Fano variety, that is, a variety X with ample anticanonical sheaf OX(−KX).
special varieties and classification theory
 Ann. Inst. Fourier
"... Abstract: A new class of compact Kähler manifolds, called special, is defined: they are the ones having no fibration with base an orbifold of general type, the orbifold structure on the base being defined by the multiple fibres of the fibration (see §1). The special manifolds are in many respect hig ..."
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Cited by 34 (0 self)
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Abstract: A new class of compact Kähler manifolds, called special, is defined: they are the ones having no fibration with base an orbifold of general type, the orbifold structure on the base being defined by the multiple fibres of the fibration (see §1). The special manifolds are in many respect higherdimensional generalisations of rational and elliptic curves. For example, we show that being rationally connected or having vanishing Kodaira dimension implies being special. Special manifolds can also be characterised by the absence of “Bogomolov ” sheaves, (see §(5.12)). For any compact Kähler X, we further construct a fibration cX: X → C(X), which we call its core 1, such that its fibre at the general point of X is the largest special subvariety of X passing through that point. When X is special (resp. of general type), the core is thus the constant (resp. the identity) map on X. We then conjecture and prove in low dimensions and some other cases that: 1) The core is a fibration of general type, which means that so is its base C(X), when equipped with its orbifold structure coming from the multiple fibres of cX. 2) Special manifolds have an almost abelian fundamental group.