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• W2963126502 abstract "For a separated Noetherian scheme <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with an ample family of line bundles and a non-zero-divisor <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W element-of normal upper Gamma left-parenthesis upper X comma upper L right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>W</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>Win Gamma (X,L)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of a line bundle <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=application/x-tex>L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we classify certain thick subcategories of the derived matrix factorization category <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=DMF left-parenthesis upper X comma upper L comma upper W right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mtext>DMF</mml:mtext> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>,</mml:mo> <mml:mi>W</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>textrm {DMF}(X,L,W)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the Landau–Ginzburg model <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper X comma upper L comma upper W right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>,</mml:mo> <mml:mi>W</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(X,L,W)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Furthermore, by using the classification result and the theory of Balmer’s tensor triangular geometry, we show that the spectrum of the tensor triangulated category <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis DMF left-parenthesis upper X comma upper L comma upper W right-parenthesis comma circled-times Superscript one half Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mtext>DMF</mml:mtext> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>,</mml:mo> <mml:mi>W</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:msup> <mml:mo>⊗<!-- ⊗ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(textrm {DMF}(X,L,W), otimes ^{frac {1}{2}})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is homeomorphic to the relative singular locus <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper S normal i normal n normal g left-parenthesis upper X 0 slash upper X right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>S</mml:mi> <mml:mi mathvariant=normal>i</mml:mi> <mml:mi mathvariant=normal>n</mml:mi> <mml:mi mathvariant=normal>g</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {Sing}(X_0/X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, introduced in this paper, of the zero scheme <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X 0 subset-of upper X> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mi>X</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>X_0subset X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W> <mml:semantics> <mml:mi>W</mml:mi> <mml:annotation encoding=application/x-tex>W</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
• W2963126502 created "2019-07-30" @default.
• W2963126502 creator A5008203017 @default.
• W2963126502 date "2018-08-30" @default.
• W2963126502 modified "2023-09-24" @default.
• W2963126502 title "Relative singular locus and Balmer spectrum of matrix factorizations" @default.
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• W2963126502 doi "https://doi.org/10.1090/tran/7509" @default.
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