# Towards the classification of weak Fano threefolds with ρ = 2

Joseph Cutrone; Nicholas Marshburn

Open Mathematics (2013)

- Volume: 11, Issue: 9, page 1552-1576
- ISSN: 2391-5455

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topJoseph Cutrone, and Nicholas Marshburn. "Towards the classification of weak Fano threefolds with ρ = 2." Open Mathematics 11.9 (2013): 1552-1576. <http://eudml.org/doc/269795>.

@article{JosephCutrone2013,

abstract = {In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases is proven.},

author = {Joseph Cutrone, Nicholas Marshburn},

journal = {Open Mathematics},

keywords = {Almost Fano; Weak Fano; Sarksiov Links; Threefolds; weak Fano threefold; extremal contraction; Sarkisov link},

language = {eng},

number = {9},

pages = {1552-1576},

title = {Towards the classification of weak Fano threefolds with ρ = 2},

url = {http://eudml.org/doc/269795},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Joseph Cutrone

AU - Nicholas Marshburn

TI - Towards the classification of weak Fano threefolds with ρ = 2

JO - Open Mathematics

PY - 2013

VL - 11

IS - 9

SP - 1552

EP - 1576

AB - In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases is proven.

LA - eng

KW - Almost Fano; Weak Fano; Sarksiov Links; Threefolds; weak Fano threefold; extremal contraction; Sarkisov link

UR - http://eudml.org/doc/269795

ER -

## References

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