Hyperplane sections and deformations

Bădescu, Lucian

doi:10.1007/bfb0071767

Cited by 12 publications

(17 citation statements)

References 25 publications

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“…Our theorem together with the classification of normal Gorenstein surfaces with ample anticanonical divisors describes the cases g(ff) = 0 and I.These cases have been discussed by B descu in [1]. It is easy to see that g(H) = Qo K=-CO and X is rational, g(fi) = l oeither κ = 0 or κ=-oo and X is a ^-b ndle of genus 1.…”

Section: Proposition 4 K Y + H = 0 <=> K Y + H ~mentioning

confidence: 87%

Ample Cartier divisors on normal surfaces.

1986

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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By a polarized normal surface we mean a pair (Y 9 H) of a normal projective surface over C and an ample Cartier divisor H on it. Define a graded ring:Let κ = κ (K γ + H, Y\ which is by defmition tr.deg. c jR -l or -oo in case R^C. To state the structure theorem, we introduce an example. Let F e = P((Pp>i®&ipi(-e)) and suppose e^ 2. Let n:F e -*Y e be the contraction of the base section b, a (-e)-curve, and let / denote the image of a fibre/on F e . Then π*/=/+-fr and 6.It turns out that H e = el is an ample Cartier divisor on y e and we haveWe shall prove the following two structure theorems.

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Section: Proposition 4 K Y + H = 0 <=> K Y + H ~mentioning

confidence: 87%

Ample Cartier divisors on normal surfaces.

1986

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…For this, another two groups of equations are invoked. The first group is the law of conservation of mass in the form of material balance equations: (13) where ν ij is the stoichiometric coefficient reflecting the content in component i of a number of specificities of…”

Section: Equations Of the Law Of Conservation Of Massmentioning

confidence: 99%

“…Thus, crown ethers [2][3][4][5][6][7][8][9]; phosphoryl containing macrocy cles [10,11]; cryptands [12][13][14][15][16][17][18]; podands [19][20][21][22][23][24]; calyxarenes, cyclodextrins, and porphyrins [25]; and phthalocyanines [26] can form complexes with highly different stabilities and stoichiometries. These com plexes are held together by noncovalent interactions with both charged and neutral chemical species in solutions [3,5,9].…”

Section: Introductionmentioning

confidence: 99%

Supramolecular complexes: Determination of stability constants on the basis of various experimental methods

Соловьев

Tsivadze

2015

Prot Met Phys Chem Surf

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Stability constants and formation enthalpies of supramolecular complexes of crown ethers and their cyclic and acyclic analogues are determined on the basis of experimental data obtained by different physicochemical methods in the terms of a general approach developed and implemented in the ChemEqui software package. The established regularities of variation of stability of complexes are discussed as dependent on the ligand structure, nature of the cation, solvent, and anion. The applicability of the suggested method of determining complexation selectivity is shown for multicomponent equilibria in solutions.

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“…The proof is computational and relies on Propositions 2.20 and 2.21 in [1][2][3][4][5][6][7][8][9][10][11][12], taking into account that e I> -2 (cf. The proof is computational and relies on Propositions 2.20 and 2.21 in [1][2][3][4][5][6][7][8][9][10][11][12], taking into account that e I> -2 (cf.…”

Section: Case D = 5 Proposition 1 If Y C Pn With N >> 4 Is a Non-nomentioning

confidence: 99%

“…If Y is a geometrically ruled surface over a curve of genus 3 with e = 0, and/-/~ C O + p'b, where b is a divisor of degree 3 on C (we employ the same notations as above), from the same exact sequence (2), it follows that h°(~0¢(/-/)) ~< 4, and this case is excluded.…”

Section: Suppose First That H°(oc(b)) = Hl(oc(b)) =mentioning

confidence: 99%

Non-normal surfaces of degree 5 and 6 in P n

Halanay¹

1989

Geom Dedicata

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The purpose of this paper is to describe the non-normal surfaces of degree 5 and 6 embedded in the complex projective space P", with n i> 4. The idea is to study the normalization of such a surface, and then to find how a non-normal surface can be obtained from its normalization.Let Yc Pn be a surface of degree d, linearly normal and not contained in any hyperplane of P~. If d ~< 4, the list of all such surfaces is known (cf. 1-23], [24]). If 5 ~< d ~< 8 and Y is smooth, the classification is also known (cf.[15], 1-16]). The list of all normal singular surfaces of degree 5 and 6 is given in [10] and [11]. The purpose of this paper is to describe the non-normal surfaces of degree 5 and 6 embedded in P~.

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Hyperplane sections and deformations

Cited by 12 publications

References 25 publications

Ample Cartier divisors on normal surfaces.

Ample Cartier divisors on normal surfaces.

Supramolecular complexes: Determination of stability constants on the basis of various experimental methods

Non-normal surfaces of degree 5 and 6 in P n

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