Mihnea Popa

Carol Davila University of Medicine and Pharmacy

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Mircea Mustaţǎ

University of Michigan–Ann Arbor

Christian Schnell

Stony Brook University

Giuseppe Pareschi

University of Rome Tor Vergata

Robert Lazarsfeld

Stony Brook University

Lawrence Ein

University of Illinois Chicago

Vlad Tudor Popa

Romanian Academy

Michael Nakamaye

University of New Mexico

Cătălin Cîrstoiu

Clinical Emergency Hospital Bucharest

Gavril Farkas

Humboldt-Universität zu Berlin

Sebastián Olano

University of Toronto

Cooperative Institutions

Carol Davila University of Medicine and Pharmacy

Clinical Emergency Hospital Bucharest

University of Michigan–Ann Arbor

Emergency University

Romanian Academy

Harvard University

Amita Health St. Mary's Hospital

Bucharest Emergency University Hospital

University of Illinois Chicago

Massachusetts Institute of Technology

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Derived invariance of the number of holomorphic 1-forms and vector fields

arXiv (Cornell University) (2009)

Mihnea Popa Christian Schnell

We prove that smooth projective varieties with equivalent derived categories have isogenous (and sometimes isomorphic) Picard varieties. In particular their irregularity and number of independent vector fields are the same. This is turn implies, in combination with the invariance of Hochschild homology, that all Hodge numbers are the same for arbitrary derived equivalent threefolds.

Hochschild homology

Homology

10.48550/arxiv.0912.4040

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[Microcalorimetry -- a new method for bacterial characterisation].

PubMed (2014)

Dragoş Zaharia Mihnea Popa Alexandru Tudor Steriade Alexandru Muntean Octavian Balint

The microcalorimetry is a method used for recording of the heat produced by a thermodinamic system in a scale of micronanojouls. One of the domains in which this method is used is the one called bacterial microcalorimetry, which studies the heat generated by the bacterial populations. The process of bacterial growth can be monitored in real time by the recording a graph of the generated power over time. The modern isothermal microcalorimeters allow the detection of a signal variation of only one microwatt. The estimated generated power of a bacteria is approximately 1-4pW thus only a small number of bacteria is necessary for the experiments. Recent studies in the field of bacterial microcalorimetry have demonstrated that, in standard conditions, this method can be reproductible and can be used to detect and characterize bacterial growth (through the study of the microcalorimetric growth curve particular to a bacterial species which is called a microcalorimetric fingerprint) and offers the new information in regards to bacterial metabolism. Also, microcalorimetry can offer information about bacterial interaction with different factors in the medium (for example, antibioticsubstances, in which case an antibiogram is obtained in 4-5 hours). In conclusion, we can say that microcalorimetry is a reproducible method, which offers an interesting perspective on bacterial characterization, with great scientific potential, and there are sufficient arguments to continue studies in this field.

Isothermal microcalorimetry

Bacterial growth

Microbial Metabolism

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Generalized theta linear series on moduli spaces of vector bundles on curves

arXiv (Cornell University) (2007)

Mihnea Popa

This article is based on lecture notes prepared for the August 2006 Cologne Summer School. The first part contains background material and references for beginners. The second (and main) part is a survey of the current status in the theory of pluri-theta linear series and generalized theta divisors on moduli spaces of vector bundles on curves. It emphasizes relatively new techniques employed in the analysis of linear series on these moduli spaces, namely the use of moduli spaces of stable maps for understanding Quot schemes, and the Fourier-Mukai functor in the study of coherent sheaves on abelian varieties. In addition, it briefly describes recent important developments, most significant of which is the proof of the Strange Duality conjecture due to Belkale and Marian-Oprea.

Duality (order theory)

10.48550/arxiv.0712.3192

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Restricted volumes and base loci of linear series

American Journal of Mathematics (2009)

Lawrence Ein Robert Lazarsfeld Mircea Mustaţǎ Michael Nakamaye Mihnea Popa

We introduce and study the restricted volume of a divisor along a subvariety. Our main result is a description of the irreducible components of the augmented base locus by the vanishing of the restricted volume.

Subvariety

Base (topology)

10.1353/ajm.0.0054

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Citations (174)

Asymptotic invariants of line bundles

arXiv (Cornell University) (2005)

Lawrence Ein Robert Lazarsfeld Mircea Mustaţǎ Michael Nakamaye Mihnea Popa

Let X be a smooth complex projective variety of dimension d. It is classical that ample line bundles on X satisfy many beautiful geometric, cohomological, and numerical properties that render their behavior particularly tractable. By contrast, examples due to Cutkosky and others have led to the common impression that the linear series associated to non-ample divisors are in general mired in pathology. However starting with fundamental work of Fujita, Nakayama, and Tsuji, it has recently become apparent that arbitrary effective (or "big") divisors in fact display a surprising number of properties analogous to those of ample line bundles. The key is to study the properties in question from an asymptotic perspective. At the same time, many interesting questions and open problems remain. The purpose of the present expository note is to give an invitation to this circle of ideas. In the hope that this informal overview might serve as a jumping off point for the technical literature in the area, we sketch many examples but provide no proofs. We focus on one particular invariant -- the "volume" of a line bundle -- that measures the rate of growth of the number of sections of powers of the bundle in question.

Line (geometry)

10.48550/arxiv.math/0505054

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Canonical cohomology as an exterior module

arXiv (Cornell University) (2010)

Robert Lazarsfeld Mihnea Popa Christian Schnell

We show that the total cohomology of the canonical bundle of a smooth projective variety, seen as a module over an exterior algebra, splits into a natural direct sum of submodules which are generated in degree zero and have a linear free resolution. This improves a previous result of the first two authors.

Projective variety

Zero (linguistics)

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Positivity for Hodge modules and geometric applications

arXiv (Cornell University) (2016)

Mihnea Popa

This is a survey of vanishing and positivity theorems for Hodge modules, and their recent applications to birational and complex geometry, expanding on my lecture at the 2015 AMS Summer Institute.

10.48550/arxiv.1605.08093

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Hodge filtration, minimal exponent, and local vanishing

Inventiones mathematicae (2019)

Mircea Mustaţǎ Mihnea Popa

Hypersurface

Filtration (mathematics)

Exponent

10.1007/s00222-019-00933-x

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Regularity on abelian varieties III: further applications

arXiv (Cornell University) (2003)

Giuseppe Pareschi Mihnea Popa

In the present sequel to our previous two papers on regularity on abelian varieties, we give a number of new applications of the theory of $M$-regularity to the study of Seshadri constants, Picard bundles, pluricanonical maps on irregular varieties, and semihomogeneous vector bundles.

Constant (computer programming)

10.48550/arxiv.math/0306103

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Injectivity and Vanishing for the Du Bois Complexes of Isolated Singularities

arXiv (Cornell University) (2024)

Mihnea Popa Wanchun Shen Anh Duc Vo

We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties. Besides some extensions and conjectures in the non-isolated case, we also provide analogues for intersection complexes.

Vanishing point

10.48550/arxiv.2409.18019

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