Symplectic geography in dimension 8.

Pasquotto, Federica

doi:10.1007/s00229-004-0533-2

Cited by 3 publications

(7 citation statements)

References 12 publications

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“…In this section we summarize Pasquotto's results. Details can be found in [13]. The Riemann-Roch theorem gives relations which a system of integers must satisfy in order to appear as the system of Chern numbers of an almost complex manifold.…”

Section: Pasquotto's Resultsmentioning

confidence: 99%

“…Let (a, j, k, m, b) be the quintuple which are related to Chern numbers as in [13]. M 8 is a connected, symplectic manifold which satisfies the quintuple (a, j, k, m, b).…”

Section: Symplectic Spin Manifoldsmentioning

confidence: 99%

“…Let M be the symplectic 8 -dimensional manifold constructed by Pasquotto in [13]. We consider the constructions in two cases.…”

Section: Example 310 (8-manifolds Constructed By Pasquotto)mentioning

confidence: 99%

“…In this article, we prove certain results on the existence of symplectic 8-manifolds with Spin(7)-structures and give some examples. Some of our results heavily depend on the work of Pasquotto [13] where she constructs 8-dimensional symplectic manifolds for every Chern number system which satisfies certain modular equations.…”

Section: Introductionmentioning

confidence: 99%

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On symplectic 8-manifolds admitting Spin(7)-structure

Yalcinkaya¹,

Ünal²

2020

Turk J Math

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Section: Pasquotto's Resultsmentioning

confidence: 99%

“…Let (a, j, k, m, b) be the quintuple which are related to Chern numbers as in [13]. M 8 is a connected, symplectic manifold which satisfies the quintuple (a, j, k, m, b).…”

Section: Symplectic Spin Manifoldsmentioning

confidence: 99%

“…Let M be the symplectic 8 -dimensional manifold constructed by Pasquotto in [13]. We consider the constructions in two cases.…”

Section: Example 310 (8-manifolds Constructed By Pasquotto)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On symplectic 8-manifolds admitting Spin(7)-structure

Yalcinkaya¹,

Ünal²

2020

Turk J Math

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“…(1) This blow-up formula was used by the second author in [12] to solve the geography problem for symplectic 8-manifolds.…”

Section: The Blow-up Formulamentioning

confidence: 99%

A formula for the Chern classes of symplectic blow-ups

Geiges¹,

Pasquotto²

2007

Journal of the London Mathematical Society

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It is shown that the formula for the Chern classes (in the Chow ring) of blow‐ups of algebraic varieties, due to Porteous and Lascu–Scott, also holds (in the singular cohomology ring) for blow‐ups of symplectic and complex manifolds. This was used by the second author in her solution of the geography problem for 8‐dimensional symplectic manifolds. The proof equally applies to real blow‐ups of arbitrary manifolds and yields the corresponding blow‐up formula for the Stiefel–Whitney classes. In the course of the argument, the topological analogue of Grothendieck’s formule clef in intersection theory is proved.

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Chern numbers and diffeomorphism types of projective varieties

Kotschick

2008

Journal of Topology

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In 1954, Hirzebruch asked which linear combinations of Chern numbers are topological invariants of smooth complex projective varieties. We give a complete answer to this question in small dimensions, and also prove partial results without restrictions on the dimension.As the right-hand side takes on only finitely many values, the same is true for c 4 1 , and then for c 2 1 c 2 as well.Remark 2. Pasquotto [9] recently raised the question of the topological invariance of Chern numbers of symplectic manifolds, particularly in (real) dimensions 6 and 8. Our results for Kähler manifolds, of course, show that Chern numbers of symplectic manifolds are not topological invariants. In the Kähler case, we have used Hodge theory to argue that the variation of Chern numbers is quite restricted, often to finitely many possibilities. It would be interesting to know whether any finiteness results hold in the symplectic non-Kähler category.

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Symplectic geography in dimension 8.

Abstract: Abstract. We show that in dimension 8 the geography of symplectic manifolds does not differ from that of almost complex ones.

Cited by 3 publications

References 12 publications

On symplectic 8-manifolds admitting Spin(7)-structure

On symplectic 8-manifolds admitting Spin(7)-structure

A formula for the Chern classes of symplectic blow-ups

Chern numbers and diffeomorphism types of projective varieties

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