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Topic: Del Pezzo surface

	Algebraic surface (Site not responding. Last check: 2007-10-21)
		In the case of geometry over the complex number field, an algebraic surface is therefore of complex dimension two (as a complex manifold) and so of dimension four as a smooth manifold.
		That is, for example, a cubic surface has a function field isomorphic to that of the projective plane, being the rational functions in two indeterminates.
		The birational geometry of algebraic surfaces is rich, because of blowing-up (also known as a monoidal transformation); under which a point is replaced by the curve of all limiting tangent directions coming into it (a projective line).
	www.free-download-soft.com /info/videochat.html (340 words)

	Del Pezzo surface (Site not responding. Last check: 2007-10-21)
		In mathematics, a del Pezzo surface is a complex two-dimensional Fano variety, i.e.
		The name is for Pasquale del Pezzo (1859-1936), an Italian mathematician from Naples.
		A Del Pezzo surface has a degree d: the projective plane case is d = 9 and the quadric case d = 8.
	www.sciencedaily.com /encyclopedia/del_pezzo_surface (266 words)

	Mysterious duality - Encyclopedia Glossary Meaning Explanation Mysterious duality (Site not responding. Last check: 2007-10-21)
		In theoretical physics, mysterious duality is a set of mathematical similarities between some objects and laws (and perhaps all of them, if the conjecture is extended appropriately) describing M-theory on k-dimensional tori (i.e.
		The main observation is that the large diffeomorphisms of del Pezzo surfaces match the Weyl group of the U-duality group of the corresponding compactification of M-theory.
		The elements of the second homology of the del Pezzo surfaces are mapped to various BPS objects of different dimensions in M-theory.
	www.encyclopedia-glossary.com /en/Mysterious-duality.html (226 words)

	Citations: Cubic forms: algebra - Yu (ResearchIndex)
		) Recall that a del Pezzo surface is a smooth surface with an ample anti canonical divisor.
		Such a surface is either P or a blowup of P at n generic points with n 8.
		Parametrization Of The Orbits Of Cubic Surfaces - Brundu (1998)
	citeseer.ist.psu.edu /context/766826/0 (1024 words)

	4a
		Del Pezzo surface : A Del Pezzo surface is a Fano variety of dimension two.
		Enriques Surface : A quotient of a K3 surface by a fixed-point free involution.
		A Fano variety of dimension two is also called a Del Pezzo surface.
	www.aimath.org /WWN/qptsurface2/articles/html/4a (1057 words)

	Surfaces de del Pezzo sans point rationnel sur un corps de dimension cohomologique un, by Jean-Louis Colliot-Thelene ... (Site not responding. Last check: 2007-10-21)
		Surfaces de del Pezzo sans point rationnel sur un corps de dimension cohomologique un, by Jean-Louis Colliot-Thelene and David Madore
		For each integer d=2,3,4, there exists a field F with cohomological dimension 1 and a del Pezzo surface of degree d over F having no rational point.
		Proofs use the theorem of Merkur'ev and Suslin, the Riemann-Roch theorem on a surface and Rost's degree formula.
	www.math.uiuc.edu /K-theory/0633 (85 words)

	abstract math/0009192 (Site not responding. Last check: 2007-10-21)
		Using lines and rulings on any such surface, we describe various representation bundles corresponding to fundamental representations of the corresponding Lie algebra.
		When we specify a geometric structure on the surface to reduce the Lie algebra to a smaller one, then the classical geometry of the configuration of lines and rulings is encoded beautifully by the branching rules in Lie theory.
		When we degenerate the surface to a non-normal del Pezzo surface, we discover that the configurations of lines and rulings are also governed by certain branching rules.
	www.math.umn.edu /~leung/Papers/ADEbundle/ADEbundle.htm (115 words)

	octonionic del Pezzo surface? (Site not responding. Last check: 2007-10-21)
		From JB's postings and a little bit of research I understand that the octonionic projective space OP^2 is an interesting "sporadic" object.
		The reason for the inquiry is that there have been attempts to identify the exceptional symmetries of the usual complex del Pezzo surface with the U-duality symmetries which occur in toroidal compactification of M-theory.
		Next by thread: Re: octonionic del Pezzo surface?
	www.lns.cornell.edu /spr/2003-06/msg0052250.html (106 words)

	EnergyStorm - Chaotic Duality In String Theory
		The gauge theories we study arise as the world-volume theory on a set of D-branes at a Calabi-Yau singularity where a del Pezzo surface shrinks to zero size.
		For a gauge theory where the del Pezzo is the Hirzebruch zero surface, the dependence of the duality wall height on the couplings at some point in the cascade has a self-similar fractal structure.
		For a gauge theory dual to P{sup 2} blown up at a point, we find periodic and quasiperiodic behavior for the gauge theory couplings that does not violate the a conjecture.
	www.energystorm.us /Chaotic_Duality_In_String_Theory-r12519.html (198 words)

	Del Mar - Encyclopedia Glossary Meaning Explanation Del Mar (Site not responding. Last check: 2007-10-21)
		Del Mar - Encyclopedia Glossary Meaning Explanation Del Mar.
		Del Mar is the name of several places in the United States of America:
		The orginal Del Mar article can be editet
	www.encyclopedia-glossary.com /en/Del-Mar.html (90 words)

	Citations: On Compact Four-Dimensional Einstein Manifolds - Hitchin (ResearchIndex)
		We note that for any log del Pezzo surface Z that both the topological Euler....
		Thus, the existence of smooth manifolds homeomorphic but not diffeomorphic to the K3 surface, which is known from Donaldson theory [11] and also follows easily from....
		In dimension four Einstein metric may not be locally symmetric, for instance the K3 surface with Yau s metric [Y] is not locally symmetric.
	citeseer.ist.psu.edu /context/48951/0 (1719 words)

	List of publications (Reinie Erné) (Site not responding. Last check: 2007-10-21)
		Construction of a del Pezzo surface with maximal Galois action on its Picard group.
		of a del Pezzo surface of degree 2 (P^2 blown up in 7 points) over the rational integers, with maximal Galois action on the Picard group of the generic fibre.
		This construction is based on one for a del Pezzo surface of degree 3 with the same property given by Torsten Ekedahl in his article
	www.math.leidenuniv.nl /~erne/wiskunde/listeng.html (246 words)

	Kunyavskij, Skorobogatov, Tsfasman: Del Pezzo surfaces of degree four
		Kunyavskij, Skorobogatov, Tsfasman: Del Pezzo surfaces of degree four
		; Skorobogatov, A. Tsfasman, M. Del Pezzo surfaces of degree four.
		— Combinatorics and geometry of Del Pezzo surfaces of degree 4, Uspekhi Mat.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=MSMF_1989_2_37__1_0 (492 words)

	Abstract delPezzo article (Reinie Erné) (Site not responding. Last check: 2007-10-21)
		Construction of a del Pezzo surface with maximal Galois action on its Picard group (JPAA 1242) - abstract
		Abstract A del Pezzo surface of degree d over a field K is a smooth projective surface X over K such that there exists
		used to prove the main result of that article, he constructs a del Pezzo surface of degree 3 over Qbar (a cubic surface)
	www.math.leidenuniv.nl /~erne/wiskunde/abstractdp.html (128 words)

	Re: octonionic del Pezzo surface? (Site not responding. Last check: 2007-10-21)
		I know everything about the octonions - well, at least compared to most people - but I have never heard of an octonionic version of the "blow-up" construction in algebraic geometry.
		The only thing I know about del Pezzo surfaces is that they are surfaces named after a guy called "del Pezzo".
		If you were looking for a category of 8-dimensional manifolds that are more special than Kaehler manifolds or hyperKaehler manifolds, I'd suggest you try octonionic manifolds: http://math.ucr.edu/home/baez/week193.html But if you want a natural category of 8n-dimensional manifolds that includes OP^2, I can't help you!
	www.lns.cornell.edu /spr/2003-06/msg0052345.html (233 words)

	Atlas: Computing the Brauer obstruction on del Pezzo surfaces of degree 4 by Adam Logan (Site not responding. Last check: 2007-10-21)
		Atlas: Computing the Brauer obstruction on del Pezzo surfaces of degree 4 by Adam Logan
		I describe a program to compute the Brauer group of a del Pezzo surface of degree 4 over the rationals and the obstruction to rational points that it yields.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caok-25.
	atlas-conferences.com /cgi-bin/abstract/caok-25 (81 words)

	Representation theory seminar Fall 2004 (Site not responding. Last check: 2007-10-21)
		We prove that $H(t,q)$ is the universal deformation of the twisted group algebra of $G$, and that this deformation is compatible with certain filtrations on $C[G]$.
		If $q$ is a root of unity, then for generic $t$ the algebra $H(t,q)$ is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface.
		For generic $q$, the spherical subalgebra $eH(t,q)e$ provides a quantization of such surfaces.
	www.math.uiuc.edu /~rinat/repth.html (193 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The gauge theory is the low energy effective theory of N D3-branes at the tip of the complex cone over the first del Pezzo surface.
		By carefully taking into account the subtle issue of flavor symmetry breaking at the fixed point, we show, using a-maximization, that this theory has in fact irrational central charge and R-charges.
		Along analogous lines, we make novel predictions for the still unknown AdS dual of the quiver theory for the second del Pezzo surface.
	www.thphys.uni-heidelberg.de /cgi-bin/abstracts/hep-th:0411249 (127 words)

	Talk 3991 data/Fall_2001/1008 (Site not responding. Last check: 2007-10-21)
		We study four N=1 SU(N)^6 gauge theories, with bi-fundamental chiral matter and a superpotential.
		In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP_3 which is the blowup of P^2 at three generic points.
		Therefore, the four gauge theories are expected to fall into the same universality class--an example of a phenomenon that has been termed "toric duality." However, little independent evidence has been given that such theories are infrared-equivalent.
	www.math.duke.edu /mcal?abstract-3991 (170 words)

	String Theory Seminars, Spring 2001 (Site not responding. Last check: 2007-10-21)
		We study four N=1 SU(N) gauge theories, with bi-fundamental chiral matter and a superpotential.
		In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP
		Therefore, the four gauge theories are expected to fall into the same universality class - an example of a phenomenon that has been termed "toric duality".
	www.physics.unc.edu /string/abs_plesser.html (153 words)

	del Pezzo \| Musings
		In the purely gauge-theoretic context, it’s a bit of a fl art to construct Seiberg dual pairs of gauge theories.
		A stringy context in which a large class of examples can be found, and hence where one can hope to find a systematic understanding, is D-branes on local del Pezzo surfaces.
		be the noncompact Calabi-Yau 3-fold, which is the total space of the canonical bundle of a del Pezzo surface,
	golem.ph.utexas.edu /~distler/blog/archives/000364.html (434 words)

	AIF : Tome 51 fascicle 1 -- 2001 (Site not responding. Last check: 2007-10-21)
		Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces
		We determine all anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces.
		Many of these admit a Kähler-Einstein metric and most of them do not have tigers.
	annalif.ujf-grenoble.fr /Vol51/E511_4/E511_4.html (85 words)

	Portugaliæ Mathematica, Vol. 57, No. 1, pp. 59-95, 2000 (Site not responding. Last check: 2007-10-21)
		Lines on Del Pezzo Surfaces with $K_{S}^{2}=1$ in Characteristic 2 in The Smooth Case
		Abstract: In the case when the branch divisor of the antibicanonical map is smooth, we prove the existence in characteristic $2$ of 240 $(-1)$-curves on a smooth projective surface with $q=0$, $K_{S}^{2}=1$, ${-}K_{S}$ ample and containing an irreducible reduced curve, concluding in this case the proof of Castelnuovo's criterion of rationality.
		This page was last modified: 31 Jan 2003.
	www.zblmath.fiz-karlsruhe.de /exx/journals/PM/57f1/6.html (87 words)

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