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RISS 인기검색어
- 검색키워드
- 저자 : Przyjalkowski, Victor (검색결과 3 건)
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LAURENT PHENOMENON FOR LANDAU-GINZBURG MODELS OF COMPLETE INTERSECTIONS IN GRASSMANNIANS OF PLANES
Przyjalkowski, Victor,Shramov, Constantin Korean Mathematical Society 2017 대한수학회보 Vol.54 No.5
In a spirit of Givental's constructions Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested Landau-Ginzburg models for smooth Fano complete intersections in Grassmannians and partial flag varieties as certain complete intersections in complex tori equipped with special functions called superpotentials. We provide a particular algorithm for constructing birational isomorphisms of these models for complete intersections in Grassmannians of planes with complex tori. In this case the superpotentials are given by Laurent polynomials. We study Givental's integrals for Landau-Ginzburg models suggested by Batyrev, Ciocan-Fontanine, Kim, and van Straten and show that they are periods for pencils of fibers of maps provided by Laurent polynomials we obtain. The algorithm we provide after minor modifications can be applied in a more general context.
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Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians of planes
Victor Przyjalkowski,Constantin Shramov 대한수학회 2017 대한수학회보 Vol.54 No.5
In a spirit of Givental's constructions Batyrev, Ciocan-Fonta\-nine, Kim, and van Straten suggested Landau--Ginzburg models for smoo\-th Fano complete intersections in Grassmannians and partial flag varieties as certain complete intersections in complex tori equipped with special functions called superpotentials. We provide a particular algorithm for constructing birational isomorphisms of these models for complete intersections in Grassmannians of planes with complex tori. In this case the superpotentials are given by Laurent polynomials. We study Givental's integrals for Landau--Ginzburg models suggested by Batyrev, Ciocan-Fontanine, Kim, and van Straten and show that they are periods for pencils of fibers of maps provided by Laurent polynomials we obtain. The algorithm we provide after minor modifications can be applied in a more general context.
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Double Solids, Categories and Non-Rationality
Iliev, Atanas,Katzarkov, Ludmil,Przyjalkowski, Victor Cambridge University Press 2014 Proceedings of the Edinburgh Mathematical Society Vol.57 No.1
<B>Abstract</B><P>This paper suggests a new approach to questions of rationality of 3-folds based on category theory. Following work by Ballard <I>et al.</I>, we enhance constructions of Kuznetsov by introducing Noether-Lefschetz spectra: an interplay between Orlov spectra and Hochschild homology. The main goal of this paper is to suggest a series of interesting examples where the above techniques might apply. We start by constructing a sextic double solid <I>X</I> with 35 nodes and torsion in <I>H</I><SUP>3</SUP>(<I>X, ℤ</I>). This is a novelty: after the classical example of Artin and Mumford, this is the second example of a Fano 3-fold with a torsion in the third integer homology group. In particular, <I>X</I> is non-rational. We consider other examples as well: <I>V</I>10 with 10 singular points, and the double covering of a quadric ramified in an octic with 20 nodal singular points. After analysing the geometry of their Landau-Ginzburg models, we suggest a general non-rationality picture based on homological mirror symmetry and category theory.</P>
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