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1. |
Record Nr. |
UNINA9910960019203321 |
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Autore |
Gross Mark |
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Titolo |
Theta Functions on Varieties with Effective Anti-Canonical Class |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2022 |
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©2022 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (122 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.278 |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Functions, Theta |
Surfaces, Algebraic |
Mirror symmetry |
Calabi-Yau manifolds |
Algebraic geometry -- Surfaces and higher-dimensional varieties -- Mirror symmetry |
Algebraic geometry -- Surfaces and higher-dimensional varieties -- Calabi-Yau manifolds |
Algebraic geometry -- Surfaces and higher-dimensional varieties -- Fano varieties |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Cover -- Title page -- Introduction -- Chapter 1. The affine geometry of the construction -- 1.1. Polyhedral affine pseudomanifolds -- 1.2. Convex, piecewise affine functions -- Chapter 2. Wall structures -- 2.1. Construction of ₀ -- 2.2. Monomials, rings and gluing morphisms -- 2.3. Walls and consistency -- 2.4. Construction of \foX^{∘} -- Chapter 3. Broken lines and canonical global functions -- 3.1. Broken lines -- 3.2. Consistency and rings in codimension two -- 3.3. The canonical global functions _{ } -- 3.4. The conical case -- 3.5. The multiplicative structure -- Chapter 4. The projective case -theta functions -- 4.1. Conical affine structures -- 4.2. The cone over a polyhedral pseudomanifold -- 4.3. Theta functions and the Main Theorem -- 4.4. |
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The action of the relative torus -- 4.5. Jagged paths -- Chapter 5. Additional parameters -- 5.1. Twisting the construction -- 5.2. Twisting by gluing data -- Chapter 6. Abelian varieties and other examples -- Appendix A. The GS case -- A.1. One-parameter families -- A.2. The universal formulation -- A.3. Equivariance -- A.4. The non-simple case in two dimensions -- Bibliography -- Back Cover. |
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Sommario/riassunto |
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"We show that a large class of maximally degenerating families of n-dimensional polarized varieties comes with a canonical basis of sections of powers of the ample line bundle. The families considered are obtained by smoothing a reducible union of toric varieties governed by a wall structure on a real n-(pseudo-)manifold. Wall structures have previously been constructed inductively for cases with locally rigid singularities [Gross and Siebert, From real affine geometry to complex geometry (2011)] and by Gromov-Witten theory for mirrors of log Calabi-Yau surfaces and K3 surfaces [Gross, Pandharipande and Siebert, The tropical vertex ; Gross, Hacking and Keel, Mirror symmetry for log Calabi-Yau surfaces (2015); Gross, Hacking, Keel, and Siebert, Theta functions and K3 surfaces (In preparation)]. For trivial wall structures on the n-torus we retrieve the classical theta functions. We anticipate that wall structures can be constructed quite generally from maximal degenerations. The construction given here then provides the homogeneous coordinate ring of the mirror degeneration along with a canonical basis. The appearance of a canonical basis of sections for certain degenerations points towards a good compactification of moduli of certain polarized varieties via stable pairs, generalizing the picture for K3 surfaces [Gross, Hacking, Keel, and Siebert, Theta functions and K3 surfaces (In preparation)]. Another possible application apart from mirror symmetry may be to geometric quantization of varieties with effective anti-canonical class"-- |
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2. |
Record Nr. |
UNINA9910157777303321 |
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Autore |
Correll Patricia |
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Titolo |
Late Summer, Early Spring |
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Pubbl/distr/stampa |
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Tallahassee : , : Dreamspinner Press, , 2015 |
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©2015 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (210 p.) : ill |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Sommario/riassunto |
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Hour of the Lotus General Sho Iwata is devastated when the man he secretly loves, Prince Narita, is struck with a mysterious illness. Iwata's current lover, Hiroshi, is well aware of the general's unrequited passion. But that isn't his biggest problem. His sister is Narita's favorite consort, but Hiroshi believes she has been replaced by an imposter. When they discover the true cause of the illness, they will have to battle an ancient spirit and survive. Fox HunterLord General Iwata Sho sets out in search of the mysterious Fox Hunter. When he finds his former lover, Hiroshi, he discovers a changed man, scarred inside and out and consumed by vengeance. Together with Narita's grown son Daigo, Iwata and Hiroshi pursue the malicious spirit as it leaves bloodshed in its wake. Iwata worries about what will become of Hiroshi when the fox is defeated--if Hiroshi's revenge doesn't kill him first. |
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