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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Cheltsov, Ivan, and Jihun Park. "Birationally rigid Fano threefold hypersurfaces." Memoirs of the American Mathematical Society 246, no. 1167 (March 2017): 0. http://dx.doi.org/10.1090/memo/1167.

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2

Polishchuk, A. "Simple Helices on Fano Threefolds." Canadian Mathematical Bulletin 54, no. 3 (September 1, 2011): 520–26. http://dx.doi.org/10.4153/cmb-2010-106-x.

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Анотація:

AbstractBuilding on the work of Nogin, we prove that the braid groupB4acts transitively on full exceptional collections of vector bundles on Fano threefolds withb2= 1 andb3= 0. Equivalently, this group acts transitively on the set of simple helices (considered up to a shift in the derived category) on such a Fano threefold. We also prove that on threefolds withb2= 1 and very ample anticanonical class, every exceptional coherent sheaf is locally free.

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3

Zhang, De-Qi. "Polarized endomorphisms of uniruled varieties. With an appendix by Y. Fujimoto and N. Nakayama." Compositio Mathematica 146, no. 1 (December 21, 2009): 145–68. http://dx.doi.org/10.1112/s0010437x09004278.

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AbstractWe show that polarized endomorphisms of rationally connected threefolds with at worst terminal singularities are equivariantly built up from those on ℚ-Fano threefolds, Gorenstein log del Pezzo surfaces and ℙ1. Similar results are obtained for polarized endomorphisms of uniruled threefolds and fourfolds. As a consequence, we show that every smooth Fano threefold with a polarized endomorphism of degree greater than one is rational.

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4

Furushima, Mikio, and Noboru Nakayama. "The family of lines on the Fano threefold V5." Nagoya Mathematical Journal 116 (December 1989): 111–22. http://dx.doi.org/10.1017/s0027763000001719.

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Анотація:

A smooth projective algebraic 3-fold V over the field C is called a Fano 3-fold if the anticanonical divisor — Kv is ample. The integer g = g(V) = ½(- Kv)3 is called the genus of the Fano 3-fold V. The maximal integer r ≧ 1 such that ϑ(— Kv)≃ ℋ r for some (ample) invertible sheaf ℋ ε Pic V is called the index of the Fano 3-fold V. Let V be a Fano 3-fold of the index r = 2 and the genus g = 21 which has the second Betti number b2(V) = 1. Then V can be embedded in P6 with degree 5, by the linear system |ℋ|, where ϑ(— Kv)≃ ℋ2 (see Iskovskih [5]). We denote this Fano 3-fold V by V5.

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5

Segal, Ed, and Richard Thomas. "Quintic threefolds and Fano elevenfolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 743 (October 1, 2018): 245–59. http://dx.doi.org/10.1515/crelle-2015-0108.

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Abstract The derived category of coherent sheaves on a general quintic threefold is a central object in mirror symmetry. We show that it can be embedded into the derived category of a certain Fano elevenfold. Our proof also generates related examples in different dimensions.

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6

Cheltsov, Ivan, and Jihun Park. "Halphen pencils on weighted Fano threefold hypersurfaces." Open Mathematics 7, no. 1 (January 1, 2009): 1–45. http://dx.doi.org/10.2478/s11533-008-0056-2.

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AbstractOn a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.

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7

Faenzi, Daniele. "Bundles over the Fano Threefold V 5." Communications in Algebra 33, no. 9 (August 2005): 3061–80. http://dx.doi.org/10.1081/agb-200066116.

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8

Ishikawa, Daizo. "Weak Fano bundles on the cubic threefold." Manuscripta Mathematica 149, no. 1-2 (June 9, 2015): 171–77. http://dx.doi.org/10.1007/s00229-015-0763-5.

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9

CIOLLI, GIANNI. "ON THE QUANTUM COHOMOLOGY OF SOME FANO THREEFOLDS AND A CONJECTURE OF DUBROVIN." International Journal of Mathematics 16, no. 08 (September 2005): 823–39. http://dx.doi.org/10.1142/s0129167x05003144.

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Анотація:

In the present paper the small quantum cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from ℙ3or the quadric Q3is explicitely computed. Because of systematic usage of the associativity property of quantum product only a very small and enumerative subset of Gromov–Witten invariants is needed. Then, for these threefolds the Dubrovin conjecture on the semisimplicity of quantum cohomology is proven by checking the computed quantum cohomology rings and by showing that a smooth Fano threefold X with b3(X) = 0 admits a complete exceptional set of the appropriate length.

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10

HÖRING, ANDREAS. "MINIMAL CLASSES ON THE INTERMEDIATE JACOBIAN OF A GENERIC CUBIC THREEFOLD." Communications in Contemporary Mathematics 12, no. 01 (February 2010): 55–70. http://dx.doi.org/10.1142/s0219199710003737.

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Анотація:

Let X be a smooth cubic threefold. We can associate two objects to X: the intermediate Jacobian J and the Fano surface F parametrizing lines on X. By a theorem of Clemens and Griffiths, the Fano surface can be embedded in the intermediate Jacobian and the cohomology class of its image is minimal. In this paper, we show that if X is generic, the Fano surface is the only surface of minimal class in J.

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11

Roulleau, Xavier. "The Fano surface of the Klein cubic threefold." Journal of Mathematics of Kyoto University 49, no. 1 (2009): 113–29. http://dx.doi.org/10.1215/kjm/1248983032.

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12

Krämer, Thomas. "Summands of theta divisors on Jacobians." Compositio Mathematica 156, no. 7 (July 2020): 1457–75. http://dx.doi.org/10.1112/s0010437x20007204.

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Анотація:

We show that the only summands of the theta divisor on Jacobians of curves and on intermediate Jacobians of cubic threefolds are the powers of the curve and the Fano surface of lines on the threefold. The proof only uses the decomposition theorem for perverse sheaves, some representation theory and the notion of characteristic cycles.

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13

Iliev, A., and D. Markushevich. "The Abel-Jacobi map for cubic threefold and periods of Fano threefolds of degree $14$." Documenta Mathematica 5 (2000): 23–47. http://dx.doi.org/10.4171/dm/74.

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14

Okada, Takuzo. "Birational Mori fiber structures of ℚ-Fano 3-fold weighted complete intersections, II". Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, № 738 (1 травня 2018): 73–129. http://dx.doi.org/10.1515/crelle-2015-0054.

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Анотація:

Abstract In [T. Okada, Birational Mori fiber structures of \mathbb{Q} -Fano 3-fold weighted complete intersection, Proc. Lond. Math. Soc. (3) 109 2014, 6, 1549–1600], we proved that, among 85 families of \mathbb{Q} -Fano threefold weighted complete intersections of codimension two, 19 families consist of birationally rigid varieties and the remaining families consists of birationally non-rigid varieties. The aim of this paper is to study systematically the remaining families and prove that every quasismooth member of 14 families is birational to another \mathbb{Q} -Fano threefold but not birational to any other Mori fiber space.

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15

Cheltsov, I. A. "Rationality of an Enriques-Fano threefold of genus five." Izvestiya: Mathematics 68, no. 3 (June 30, 2004): 607–18. http://dx.doi.org/10.1070/im2004v068n03abeh000490.

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16

GRUSON, L., F. LAYTIMI, and D. S. NAGARAJ. "ON PRIME FANO THREEFOLDS OF GENUS 9." International Journal of Mathematics 17, no. 03 (March 2006): 253–61. http://dx.doi.org/10.1142/s0129167x06003461.

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Анотація:

It is shown here that any prime Fano threefold of genus 9 is not exotic, that is, its scheme of lines is reduced at the generic point of every component. This extends a result of Prokhorov who showed that the only exotic Fano 3-fold of genus > 9 is the example of Mukai–Umemura. The problem is reduced to a result, obtained here, about the trisecants of a smooth space curve of genus 3 and degree 7.

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17

Prokhorov, Yuri. "Conic bundle structures on $ \mathbb{Q} $-Fano threefolds." Electronic Research Archive 30, no. 5 (2022): 1881–97. http://dx.doi.org/10.3934/era.2022095.

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18

Krasnov, V. A. "On the Fano Surface of a Real Cubic M-Threefold." Mathematical Notes 78, no. 5-6 (November 2005): 662–68. http://dx.doi.org/10.1007/s11006-005-0169-x.

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19

Clemens, Herbert, and Stuart Raby. "$F$-theory over a Fano threefold built from $A_4$-roots." Advances in Theoretical and Mathematical Physics 26, no. 2 (2022): 325–70. http://dx.doi.org/10.4310/atmp.2022.v26.n2.a3.

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20

Gounelas, Frank, and Alexis Kouvidakis. "Measures of irrationality of the Fano surface of a cubic threefold." Transactions of the American Mathematical Society 371, no. 10 (October 17, 2018): 7111–33. http://dx.doi.org/10.1090/tran/7565.

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21

Brambilla, Maria Chiara, and Daniele Faenzi. "Vector bundles on Fano threefolds of genus 7 and Brill–Noether loci." International Journal of Mathematics 25, no. 03 (March 2014): 1450023. http://dx.doi.org/10.1142/s0129167x14500232.

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Анотація:

Let X be a smooth prime Fano threefold of genus 7 and let Γ be its homologically projectively dual curve. We prove that, for d ≥ 6, an irreducible component of the moduli scheme M X(2, 1, d) of rank-2 stable sheaves on X with c1 = 1, c2 = d is birational to a generically smooth (2d - 9)-dimensional component of the Brill–Noether variety [Formula: see text] of stable vector bundles on Γ of rank d - 5 and degree 5d-24 with at least 2d - 10 independent global sections. The space M X(2, 1, 6) is proved to be isomorphic to [Formula: see text], and to be a smooth irreducible threefold if X is general enough.

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22

TRUONG, TUYEN TRUNG. "Automorphisms of blowups of threefolds being Fano or having Picard number 1." Ergodic Theory and Dynamical Systems 37, no. 7 (May 12, 2016): 2255–75. http://dx.doi.org/10.1017/etds.2016.4.

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Анотація:

Let $X_{0}$ be a smooth projective threefold which is Fano or which has Picard number 1. Let $\unicode[STIX]{x1D70B}:X\rightarrow X_{0}$ be a finite composition of blowups along smooth centers. We show that for ‘almost all’ of such $X$, if $f\in \text{Aut}(X)$, then its first and second dynamical degrees are the same. We also construct many examples of blowups $X\rightarrow X_{0}$, on which any automorphism is of zero entropy. The main idea is that, because of the log-concavity of dynamical degrees and the invariance of Chern classes under holomorphic automorphisms, there are some constraints on the nef cohomology classes. We will also discuss a possible application of these results to a threefold constructed by Kenji Ueno.

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23

Krasnov, V. A. "The Albanese map of the Fano surface of a real M-cubic threefold." Mathematical Notes 84, no. 3-4 (October 2008): 356–62. http://dx.doi.org/10.1134/s0001434608090058.

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24

Furushima, Mikio. "Mukai-Umemura’s example of the Fano threefold with genus 12 as a compactification of C3." Nagoya Mathematical Journal 127 (September 1992): 145–65. http://dx.doi.org/10.1017/s0027763000004141.

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Анотація:

Let (X, Y) be a smooth projective compactification with the non-normal irreducible boundary Y, namely, X is a smooth projective algebraic threefold and Y a non-normal irreducible divisor on X such that X – Y is isomorphic to C3. Then Y is ample and the canonical divisor Kx on X can be written as Kx = - r Y (1 ≦ r ≦ 4).

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25

Braun, Volker. "Discrete Wilson Lines in F-Theory." Advances in High Energy Physics 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/404691.

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F-theory models are constructed where the7-brane has a nontrivial fundamental group. The base manifolds used are a toric Fano variety and a smooth toric threefold coming from a reflexive polyhedron. The discriminant locus of the elliptically fibered Calabi-Yau fourfold can be chosen such that one irreducible component is not simply connected (namely, an Enriques surface) and supports a non-Abelian gauge theory.

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26

Roulleau, Xavier. "The Fano surface of the Fermat cubic threefold, the del Pezzo surface of degree $5$ and a ball quotient." Proceedings of the American Mathematical Society 139, no. 10 (October 1, 2011): 3405. http://dx.doi.org/10.1090/s0002-9939-2011-10847-5.

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27

Cutrone, Joseph W., Michael A. Limarzi, and Nicholas A. Marshburn. "A weak Fano threefold arising as a blowup of a curve of genus 5 and degree 8 on $${\mathbb {P}}^3$$ P 3." European Journal of Mathematics 5, no. 3 (February 6, 2019): 763–70. http://dx.doi.org/10.1007/s40879-019-00315-w.

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28

Prokhorov, Yu G. "On $ G$-Fano threefolds." Izvestiya: Mathematics 79, no. 4 (August 25, 2015): 795–808. http://dx.doi.org/10.1070/im2015v079n04abeh002761.

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29

Prokhorov, Yu G. "On Fano-Enriques threefolds." Sbornik: Mathematics 198, no. 4 (April 30, 2007): 559–74. http://dx.doi.org/10.1070/sm2007v198n04abeh003849.

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30

Kasprzyk, Alexander M. "Canonical Toric Fano Threefolds." Canadian Journal of Mathematics 62, no. 6 (December 14, 2010): 1293–309. http://dx.doi.org/10.4153/cjm-2010-070-3.

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Анотація:

AbstractAn inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties.

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31

Cynk, Sławomir. "Cyclic coverings of Fano threefolds." Annales Polonici Mathematici 80 (2003): 117–24. http://dx.doi.org/10.4064/ap80-0-9.

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32

Kuznetsov, Alexander. "Instanton bundles on Fano threefolds." Central European Journal of Mathematics 10, no. 4 (May 2, 2012): 1198–231. http://dx.doi.org/10.2478/s11533-012-0055-1.

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33

Kuznetsov, A. G. "Derived categories of Fano threefolds." Proceedings of the Steklov Institute of Mathematics 264, no. 1 (April 2009): 110–22. http://dx.doi.org/10.1134/s0081543809010143.

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34

Przhyjalkowski, V. V., I. A. Cheltsov, and K. A. Shramov. "Hyperelliptic and trigonal Fano threefolds." Izvestiya: Mathematics 69, no. 2 (April 30, 2005): 365–421. http://dx.doi.org/10.1070/im2005v069n02abeh000533.

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35

Logachev, Dmitry. "Fano threefolds of Genus 6." Asian Journal of Mathematics 16, no. 3 (2012): 515–59. http://dx.doi.org/10.4310/ajm.2012.v16.n3.a9.

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36

OXBURY, W. M. "TWISTOR SPACES AND FANO THREEFOLDS." Quarterly Journal of Mathematics 45, no. 3 (1994): 343–66. http://dx.doi.org/10.1093/qmath/45.3.343.

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37

Amerik, Ekaterina. "Maps onto certain Fano threefolds." Documenta Mathematica 2 (1997): 195–211. http://dx.doi.org/10.4171/dm/28.

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38

Prokhorov, Yuri G. "Fano threefolds of large Fano index and large degree." Sbornik: Mathematics 204, no. 3 (March 31, 2013): 347–82. http://dx.doi.org/10.1070/sm2013v204n03abeh004304.

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39

Prokhorov, Yuri. "$\Bbb Q$-Fano threefolds of large Fano index. I." Documenta Mathematica 15 (2010): 843–72. http://dx.doi.org/10.4171/dm/316.

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40

Iliev, Atanas, and Carmen Schuhmann. "Tangent scrolls in prime Fano threefolds." Kodai Mathematical Journal 23, no. 3 (2000): 411–31. http://dx.doi.org/10.2996/kmj/1138044268.

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41

Lee, Seunghun. "Linear Systems on Fano Threefolds. I." Communications in Algebra 32, no. 7 (December 31, 2004): 2711–21. http://dx.doi.org/10.1081/agb-120037411.

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42

Prokhorov, Yuri G. "ℚ-Fano threefolds of index 7". Proceedings of the Steklov Institute of Mathematics 294, № 1 (серпень 2016): 139–53. http://dx.doi.org/10.1134/s0081543816060092.

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43

Przyjalkowski, V. V., I. A. Cheltsov, and K. A. Shramov. "Fano threefolds with infinite automorphism groups." Izvestiya: Mathematics 83, no. 4 (August 2019): 860–907. http://dx.doi.org/10.1070/im8834.

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44

Prokhorov, Yu G. "Singular Fano threefolds of genus 12." Sbornik: Mathematics 207, no. 7 (July 31, 2016): 983–1009. http://dx.doi.org/10.1070/sm8585.

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45

Cavalcante, Alana, Mauricio Corrêa, and Simone Marchesi. "On holomorphic distributions on Fano threefolds." Journal of Pure and Applied Algebra 224, no. 6 (June 2020): 106272. http://dx.doi.org/10.1016/j.jpaa.2019.106272.

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46

LAI, CHING-JUI. "BOUNDING VOLUMES OF SINGULAR FANO THREEFOLDS." Nagoya Mathematical Journal 224, no. 1 (October 17, 2016): 37–73. http://dx.doi.org/10.1017/nmj.2016.21.

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Анотація:

Let $(X,\unicode[STIX]{x1D6E5})$ be an $n$-dimensional $\unicode[STIX]{x1D716}$-klt log $\mathbb{Q}$-Fano pair. We give an upper bound for the volume $\text{Vol}(X,\unicode[STIX]{x1D6E5})=(-(K_{X}+\unicode[STIX]{x1D6E5}))^{n}$ when $n=2$, or $n=3$ and $X$ is $\mathbb{Q}$-factorial of $\unicode[STIX]{x1D70C}(X)=1$. This bound is essentially sharp for $n=2$. The main idea is to analyze the covering families of tigers constructed in J. McKernan (Boundedness of log terminal fano pairs of bounded index, preprint, 2002, arXiv:0205214). Existence of an upper bound for volumes is related to the Borisov–Alexeev–Borisov Conjecture, which asserts boundedness of the set of $\unicode[STIX]{x1D716}$-klt log $\mathbb{Q}$-Fano varieties of a given dimension $n$.

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47

Mayanskiy, Evgeny. "Poisson cohomology of two Fano threefolds." Journal of Algebra 424 (February 2015): 21–45. http://dx.doi.org/10.1016/j.jalgebra.2014.08.049.

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48

Iliev, Atanas, and Laurent Manivel. "Prime Fano threefolds and integrable systems." Mathematische Annalen 339, no. 4 (July 27, 2007): 937–55. http://dx.doi.org/10.1007/s00208-007-0145-8.

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49

Lee, Seunghun. "Linear systems on Fano threefolds II." Mathematische Zeitschrift 248, no. 4 (May 6, 2004): 893–909. http://dx.doi.org/10.1007/s00209-004-0687-3.

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50

Jahnke, Priska, and Ivo Radloff. "Terminal Fano threefolds and their smoothings." Mathematische Zeitschrift 269, no. 3-4 (September 26, 2010): 1129–36. http://dx.doi.org/10.1007/s00209-010-0780-8.

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