On the Chern numbers of a smooth threefold

Cascini, Paolo; Tasin, Luca

doi:10.1090/tran/7216

Cited by 10 publications

(25 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, for those smooth threefolds with the property that the process of the minimal model program consists of only divisorial contractions to points and blowing‐up smooth curves, their

c_{1}^{3}

will be bounded by topology. This is the main theorem of .…”

Section: Introductionmentioning

confidence: 81%

“…This question is trivial in dimension one and has been proved in dimension two (please see ). Cascini and Tasin have proved the statement in some special cases in dimension three, but in general this question is still open for dimension greater than two.…”

Section: Introductionmentioning

confidence: 99%

“…We will briefly introduce the result in the three‐dimensional case . One needs to show that

c_{1}^{3}

and

c_{1} . c_{2}

of a smooth threefold is bounded by a constant depending only on the topological type of the threefold.…”

Section: Introductionmentioning

confidence: 99%

“…One can see that how to estimate the change of Betti numbers under the minimal model program becomes an important issue if we want to generalize the result of into general situations. This gives the motivation of our article.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of divisorial contractions, the change of

b_{4}

b_{5}

and

b_{6}

can be studied via the long exact sequence of cohomology groups and with some knowledge in algebraic geometry it is not hard to obtain the change of

b_{1}

and

b_{2}

, cf. [, Lemmas 2.16, 2.17]. However, no tool can be used to compute

b_{3}

.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Betti numbers in the three‐dimensional minimal model program

Chen

2019

Bull. London Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Hence, for those smooth threefolds with the property that the process of the minimal model program consists of only divisorial contractions to points and blowing‐up smooth curves, their

c_{1}^{3}

will be bounded by topology. This is the main theorem of .…”

Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

“…We will briefly introduce the result in the three‐dimensional case . One needs to show that

c_{1}^{3}

and

c_{1} . c_{2}

of a smooth threefold is bounded by a constant depending only on the topological type of the threefold.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In the case of divisorial contractions, the change of

b_{4}

b_{5}

and

b_{6}

can be studied via the long exact sequence of cohomology groups and with some knowledge in algebraic geometry it is not hard to obtain the change of

b_{1}

and

b_{2}

, cf. [, Lemmas 2.16, 2.17]. However, no tool can be used to compute

b_{3}

.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Betti numbers in the three‐dimensional minimal model program

Chen

2019

Bull. London Math. Soc.

View full text Add to dashboard Cite

show abstract

Chern Numbers of Uniruled Threefolds

Schreieder

Tasin

2020

Birational Geometry and Moduli Spaces

Self Cite

View full text Add to dashboard Cite

show abstract

Kähler structures on spin 6-manifolds

Schreieder¹,

Tasin

2017

Math. Ann.

Self Cite

View full text Add to dashboard Cite

We show that many spin 6-manifolds have the homotopy type but not the homeomorphism type of a Kähler manifold. Moreover, for given Betti numbers, there are only finitely many deformation types and hence topological types of smooth complex projectve spin threefolds of general type. Finally, on a fixed spin 6-manifold, the Chern numbers take on only finitely many values on all possible Kähler structures.

show abstract

On the Chern numbers of a smooth threefold

Abstract: Abstract. We study the behaviour of Chern numbers of three dimensional terminal varieties under divisorial contractions.

Cited by 10 publications

References 32 publications

Betti numbers in the three‐dimensional minimal model program

Betti numbers in the three‐dimensional minimal model program

Chern Numbers of Uniruled Threefolds

Kähler structures on spin 6-manifolds

Contact Info

Product

Resources

About