A. A. Borisov, L. A. Borisov, “Singular toric Fano varieties”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 277

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Russian Academy of Sciences. Sbornik. Mathematics, 1993, Volume 75, Issue 1, Pages 277–283
DOI: https://doi.org/10.1070/SM1993v075n01ABEH003385 (Mi sm1470)

This article is cited in 24 scientific papers (total in 24 papers)

Singular toric Fano varieties

A. A. Borisov, L. A. Borisov

M. V. Lomonosov Moscow State University

English version PDF (401 kB) Citations (24) Russian version article

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DOI: https://doi.org/10.1070/SM1993v075n01ABEH003385

Abstract: The authors prove that the number of types of toric Fano varieties with certain constraints on the singularities is finite.

Received: 25.09.1990

Bibliographic databases:

MSC: 14J45, 14M25

Language: English

Original paper language: Russian

Citation: A. A. Borisov, L. A. Borisov, “Singular toric Fano varieties”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 277–283

Citation in format AMSBIB

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\yr 1993

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https://doi.org/10.1070/SM1993v075n01ABEH003385

https://www.mathnet.ru/eng/sm/v183/i2/p134

This publication is cited in the following 24 articles:

Ziquan Zhuang, “On boundedness of singularities and minimal log discrepancies of Kollár components”, J. Algebraic Geom., 33:3 (2024), 521
Joaquín Moraga, “Coregularity of Fano varieties”, Geom Dedicata, 218:2 (2024)
Jürgen Hausen, Christian Mauz, Milena Wrobel, “The Anticanonical Complex for Non-degenerate Toric Complete Intersections”, manuscripta math., 172:1-2 (2023), 89
C. Birkar, Y. Chen, “Singularities on toric fibrations”, Sb. Math., 212:3 (2021), 288–304
V. V. Przyjalkowski, С. A. Shramov, “Smooth Prime Fano Complete Intersections in Toric Varieties”, Math. Notes, 109:4 (2021), 609–613
Jiang Ch., “On Birational Boundedness of Fano Fibrations”, Am. J. Math., 140:5 (2018), 1253–1276
B. Bechtold, J. Hausen, E. Huggenberger, M. Nicolussi, “On Terminal Fano 3-Folds with 2-Torus Action”, International Mathematics Research Notices, 2015
Coates T., Gonshaw S., Kasprzyk A., Nabijou N., “Mutations of Fake Weighted Projective Spaces”, Electron. J. Comb., 21:4 (2014)
Averkov G., “On the Size of Lattice Simplices with a Single Interior Lattice Point”, SIAM Discret. Math., 26:2 (2012), 515–526
Prokhorov Yu., “Q-Fano Threefolds of Large Fano Index, I”, Doc Math, 15 (2010), 843–872
Kasprzyk A.M., “Canonical Toric Fano Threefolds”, Can. J. Math.-J. Can. Math., 62:6 (2010), 1293–1309
Okada T., “On the Birational Unboundedness of Higher Dimensional Q-Fano Varieties”, Math. Ann., 345:1 (2009), 195–212
Prokhorov Yu.G., Shokurov V.V., “Towards the Second Main Theorem on Complements”, J. Algebr. Geom., 18:1 (2009), 151–199
Pasquier B., “Fano Horospherical Varieties”, Bull. Soc. Math. Fr., 136:2 (2008), 195–225
Nill, B, “Volume and lattice points of reflexive simplices”, Discrete & Computational Geometry, 37:2 (2007), 301
Alexander M. Kasprzyk, “Toric Fano three-folds with terminal singularities”, Tohoku Math. J. (2), 58:1 (2006)
K. A. Shramov, “Elementary Birational Maps between Mori Toric Fiber 3-Spaces”, Math. Notes, 78:1 (2005), 120–127
McKernan, J, “Threefold thresholds”, Manuscripta Mathematica, 114:3 (2004), 281
Proc. Steklov Inst. Math., 240 (2003), 75–213
Debarre O., “Fano Varieties”, Higher Dimensional Varieties and Rational Points, Bolyai Society Mathematical Studies, 12, eds. Boroczky K., Kollar K., Szamuely T., Springer-Verlag Berlin, 2003, 93–132

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	657
Russian version PDF:	240
English version PDF:	41
References:	71
First page:	1

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