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2 y
The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the second lecture. The last two lectures are devoted to some applications of arc spaces toward a conjecture on minimal log discrepancies known as inversion of adjunction. Minimal log discrepancies are invariants of singularities appearing in the minimal model program, a quick overview of which is given in the third lecture.
[-] The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the ...
[+] 14E18 ; 14E15 ; 13A18 ; 14B05 ; 14E30
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y
The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the second lecture. The last two lectures are devoted to some applications of arc spaces toward a conjecture on minimal log discrepancies known as inversion of adjunction. Minimal log discrepancies are invariants of singularities appearing in the minimal model program, a quick overview of which is given in the third lecture.
[-] The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the ...
[+] 14E18 ; 14E15 ; 13A18 ; 14B05 ; 14E30
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
y
The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the second lecture. The last two lectures are devoted to some applications of arc spaces toward a conjecture on minimal log discrepancies known as inversion of adjunction. Minimal log discrepancies are invariants of singularities appearing in the minimal model program, a quick overview of which is given in the third lecture.
[-] The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the ...
[+] 14E18 ; 14E15 ; 13A18 ; 14B05 ; 14E30
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y
The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the second lecture. The last two lectures are devoted to some applications of arc spaces toward a conjecture on minimal log discrepancies known as inversion of adjunction. Minimal log discrepancies are invariants of singularities appearing in the minimal model program, a quick overview of which is given in the third lecture.
[-] The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the ...
[+] 14E18 ; 14E15 ; 13A18 ; 14B05 ; 14E30
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2 y
The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu.
[-] The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint ...
[+] 14B05 ; 14D06 ; 14E30 ; 14E18 ; 14G10 ; 14G22
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y
The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu.
[-] The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint ...
[+] 14B05 ; 14D06 ; 14E30 ; 14E18 ; 14G10 ; 14G22
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y
The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint work with Mircea Mustata and Chenyang Xu.
[-] The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its relations with the Minimal Model Program and Igusa's p-adic zeta functions. No prior knowledge of non-archimedean geometry is assumed. These lectures are based on joint ...
[+] 14B05 ; 14D06 ; 14E30 ; 14E18 ; 14G10 ; 14G22
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y
A principle governing deformation theory with cohomology constraints in characteristic zero, generalizing Deligne's deformation theory principle, was developed together with B. Wang, M. Rubio in terms of dg Lie modules, and, more generally, $\text{L}\infty$ modules. An application of this theory is that for a generic compact Riemann surface the theta function is at every point on the Jacobian equal to its first non-zero Taylor term, up to a holomorphic change of local coordinates and multiplication by a local holomorphic unit.
[-] A principle governing deformation theory with cohomology constraints in characteristic zero, generalizing Deligne's deformation theory principle, was developed together with B. Wang, M. Rubio in terms of dg Lie modules, and, more generally, $\text{L}\infty$ modules. An application of this theory is that for a generic compact Riemann surface the theta function is at every point on the Jacobian equal to its first non-zero Taylor term, up to a ...
[+] 14B05 ; 14H42 ; 14B12
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y
These lectures will revolve around applications of Hrushovski and Kazhdan's theory of motivic integration. It associates motivic invariants to semi-algebraic sets in algebraically closed valued fields. Following the work of Hrushovski and Loeser, and in collaboration with Yin, we shall see that when applied to the non-archimedean Milnor fiber, the motivic volumes recover some classical invariants of the Milnor fiber. Finally, we will see how these methods can be applied to a singularity arising as the quotient of a smooth variety by a linear group. When the group is finite, the orbifold formula of Batyrev and Denef–Loeser provides a motivic version of the McKay correspondence. In collaboration with Loeser and Wyss, we establish a similar formula for a general linear group.
[-] These lectures will revolve around applications of Hrushovski and Kazhdan's theory of motivic integration. It associates motivic invariants to semi-algebraic sets in algebraically closed valued fields. Following the work of Hrushovski and Loeser, and in collaboration with Yin, we shall see that when applied to the non-archimedean Milnor fiber, the motivic volumes recover some classical invariants of the Milnor fiber. Finally, we will see how ...
[+] 03C98 ; 14B05 ; 14J17 ; 32S25 ; 32S55
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y
These lectures will revolve around applications of Hrushovski and Kazhdan's theory of motivic integration. It associates motivic invariants to semi-algebraic sets in algebraically closed valued fields. Following the work of Hrushovski and Loeser, and in collaboration with Yin, we shall see that when applied to the non-archimedean Milnor fiber, the motivic volumes recover some classical invariants of the Milnor fiber. Finally, we will see how these methods can be applied to a singularity arising as the quotient of a smooth variety by a linear group. When the group is finite, the orbifold formula of Batyrev and Denef–Loeser provides a motivic version of the McKay correspondence. In collaboration with Loeser and Wyss, we establish a similar formula for a general linear group.
[-] These lectures will revolve around applications of Hrushovski and Kazhdan's theory of motivic integration. It associates motivic invariants to semi-algebraic sets in algebraically closed valued fields. Following the work of Hrushovski and Loeser, and in collaboration with Yin, we shall see that when applied to the non-archimedean Milnor fiber, the motivic volumes recover some classical invariants of the Milnor fiber. Finally, we will see how ...
[+] 03C98 ; 14B05 ; 14J17 ; 32S25 ; 32S55
English
