The Department of Mathematics has organised a mini-course on Algebraic Geometry given by Nabanita Ray and Snehajit Misra, both from the Chennai Mathematical Institute (CMI). In addition, there are two talks in the Mathematics Colloquium. Nabanita and Snehajit are visiting Ashoka University in the week of February 24.
The details of their talks are as follows.
Date : 20th Feb 2023 | Time: 5:00 PM to 6:00 PM | Venue: Lecture Room – AC04-407 | Mini-course on Algebraic Geometry
NOTE: Please note the unusual day and time.
Speaker : Nabanita Ray (CMI)
Title: Positive cones of line bundles in algebraic geometry.
Abstract: In this introductory talk we recall the definition of affine and projective varieties over complex numbers and their morphisms. Then we briefly discuss the isomorphic classes of line bundles on a variety which form an abelian group known as the Picard Group of that variety. A quotient of Picard Group by the numerically trivial line bundles is known as Neron-Severi group which is a finitely generated abelian group. Then we describe some important classes of line bundles on these varieties and convex cones generated by these line bundles inside the real Neron-Severi group.
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Date : 21st Feb 2023 | Time: 3:00 PM to 4:00 PM | Venue: Lecture Room – AC04-407 | Mini-course on Algebraic Geometry I|
NOTE: Please note that we will begin 15 minutes earlier than usual.
Speaker : Snehajit Misra (CMI)
Title: Positive Cones of Projective Bundles
Abstract : In this introductory talk, we will review the basic definitions of various positive cones inside the Real Neron-Severi group of a smooth complex projective variety. Special emphasis will be given to compute the positive cones of line bundles on projective bundles over a smooth complex projective variety. We will define the notion of vector bundles and projective bundles over smooth complex projective varieties for this purpose.
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Date : 21st Feb 2023 | Time: 4:30 PM to 5:30 PM | Venue: Lecture Room – AC04-407 | Mathematics Colloquium I
Speaker : Nabanita Ray (CMI)
Title: Weyl and Zariski chambers on projective surfaces
Abstract: Let X be a nonsingular complex projective surface. Big cone is a convex cone generated by the big classes of line bundles on the real Neron-Severi group. The Weyl and Zariski chambers give two interesting decompositions of the big cone of X. In this talk we see these two decompositions and determine when a Weyl chamber is contained in the interior of a Zariski chamber and vice versa. Moreover we describe when a Weyl chamber can intersect non-trivially with a Zariski chamber.
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Date : 23rd Feb 2023 | Time: 5:00 PM to 6:00 PM | Venue: Lecture Room – AC04-407 | Mathematics Colloquium II
NOTE: Please note the unusual day and time.
Speaker : Dr Snehajit Misra
Title : On existence of Weak Zariski decomposition on projective bundles
Abstract : Zariski introduced a decomposition on surfaces to dismantle orthogonally (pseudo-)effective divisors into positive and negative parts, both of which enjoy the useful geometric properties. Many attempts has been made to generalise this decomposition on higher dimensional varieties, for instance the Fujita-Zariski decomposition and the CKM-Zariski decomposition. Recently, a weeker notion of this decomposition has been suggested by Birkar. In this talk, we will discuss about existence of weak Zariski decomposition of pseudo-effective divisors on projective bundles over higher dimensional varieties in order to answer a question posed by Birkar.
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About Speakers:
Nabanita Ray obtained her Ph.D. from the Institute of Mathematical Sciences (I.M.Sc.) Chennai in 2019. She is currently a Post-Doctoral Fellow in the Chennai Mathematical Institute (CMI).
Snehajit Misra obtained his Ph.D. from the Institute of Mathematical Sciences (I.M.Sc.) Chennai in 2019 and did his post-doctoral work in TIFR and IIT, Bombay. Currently, he is the SERB-NPDF Postdoctoral Fellow, Chennai Mathematical Institute, Chennai.
